Counterexamples to regularity of Mañé projections in the theory of attractors

International Nuclear Information System (INIS)

Eden, Al'p; Zelik, Sergey V; Kalantarov, Varga K

2013-01-01

This paper is a study of global attractors of abstract semilinear parabolic equations and their embeddings in finite-dimensional manifolds. As is well known, a sufficient condition for the existence of smooth (at least C 1 -smooth) finite-dimensional inertial manifolds containing a global attractor is the so-called spectral gap condition for the corresponding linear operator. There are also a number of examples showing that if there is no gap in the spectrum, then a C 1 -smooth inertial manifold may not exist. On the other hand, since an attractor usually has finite fractal dimension, by Mañé's theorem it projects bijectively and Hölder-homeomorphically into a finite-dimensional generic plane if its dimension is large enough. It is shown here that if there are no gaps in the spectrum, then there exist attractors that cannot be embedded in any Lipschitz or even log-Lipschitz finite-dimensional manifold. Thus, if there are no gaps in the spectrum, then in the general case the inverse Mañé projection of the attractor cannot be expected to be Lipschitz or log-Lipschitz. Furthermore, examples of attractors with finite Hausdorff and infinite fractal dimension are constructed in the class of non-linearities of finite smoothness. Bibliography: 35 titles.

Probability Density Function Method for Observing Reconstructed Attractor Structure

Institute of Scientific and Technical Information of China (English)

陆宏伟; 陈亚珠; 卫青

2004-01-01

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6 - 6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

Science.gov (United States)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Exponential attractors for a nonclassical diffusion equation

Directory of Open Access Journals (Sweden)

Qiaozhen Ma

2009-01-01

Full Text Available In this article, we prove the existence of exponential attractors for a nonclassical diffusion equation in ${H^{2}(Omega}cap{H}^{1}_{0}(Omega$ when the space dimension is less than 4.

Plateau onset for correlation dimension: When does it occur?

International Nuclear Information System (INIS)

Ding, M.; Grebogi, C.; Ott, E.; Sauer, T.; Yorke, J.A.

1993-01-01

Chaotic experimental systems are often investigated using delay coordinates. Estimated values of the correlation dimension in delay coordinate space typically increase with the number of delays and eventually reach a plateau (on which the dimension estimate is relatively constant) whose value is commonly taken as an estimate of the correlation dimension D 2 of the underlying chaotic attractor. We report a rigorous result which implies that, for long enough data sets, the plateau begins when the number of delay coordinates first exceeds D 2 . Numerical experiments are presented. We also discuss how lack of sufficient data can produce results that seem to be inconsistent with the theoretical prediction

Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

2015-01-01

Roč. 14, č. 5 (2015), s. 1685-1704 ISSN 1534-0392 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic evolution equations * state-dependent delay * global attractor * finite-dimension * exponential attractor Subject RIV: BC - Control Systems Theory Impact factor: 0.926, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf

Localization of hidden Chua's attractors

International Nuclear Information System (INIS)

Leonov, G.A.; Kuznetsov, N.V.; Vagaitsev, V.I.

2011-01-01

The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. In the present Letter for localization of hidden attractors of Chua's circuit it is suggested to use a special analytical-numerical algorithm. -- Highlights: → There are hidden attractors: basin doesn't contain neighborhoods of equilibria. → Hidden attractors cannot be reached by trajectory from neighborhoods of equilibria. → We suggested special procedure for localization of hidden attractors. → We discovered hidden attractor in Chua's system, L. Chua in his work didn't expect this.

Strange attractor in the Potts spin glass on hierarchical lattices

Energy Technology Data Exchange (ETDEWEB)

Lima, Washington de [Universidade Federal de Pernambuco, Centro Acadêmico do Agreste, Pernambuco (Brazil); Camelo-Neto, G. [Universidade Federal de Alagoas, Núcleo de Ciências Exatas, Laboratório de Física Teórica e Computacional, CEP 57309-005 Arapiraca, Alagoas (Brazil); Coutinho, S., E-mail: sergio@ufpe.br [Universidade Federal de Pernambuco, Departamento de Física, Laboratório de Física Teórica e Computacional, Cidade Universitária, CEP 50670-901 Recife, Pernambuco (Brazil)

2013-11-29

The spin-glass q-state Potts model on d-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension d{sub l}(q) for q>2, the coupling constants probability distribution flows to a low-temperature strange attractor or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature T{sub c}(q,d). The strange attractor was investigated considering four initial different distributions for q=3 and d=5 presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.

Black hole entropy functions and attractor equations

International Nuclear Information System (INIS)

Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

2007-01-01

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

Hidden attractors in dynamical systems

Science.gov (United States)

Dudkowski, Dawid; Jafari, Sajad; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Prasad, Awadhesh

2016-06-01

Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical-numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.

Dimensions of Fractals Generated by Bi-Lipschitz Maps

Directory of Open Access Journals (Sweden)

Qi-Rong Deng

2014-01-01

Full Text Available On the class of iterated function systems of bi-Lipschitz mappings that are contractions with respect to some metrics, we introduce a logarithmic distortion property, which is weaker than the well-known bounded distortion property. By assuming this property, we prove the equality of the Hausdorff and box dimensions of the attractor. We also obtain a formula for the dimension of the attractor in terms of certain modified topological pressure functions, without imposing any separation condition. As an application, we prove the equality of Hausdorff and box dimensions for certain iterated function systems consisting of affine maps and nonsmooth maps.

Crisis-induced unstable dimension variability in a dynamical system

International Nuclear Information System (INIS)

Kubo, Geraldo T.; Viana, Ricardo L.; Lopes, Sergio R.; Grebogi, Celso

2008-01-01

Unstable dimension variability is an extreme form of non-hyperbolic behavior in chaotic systems whose attractors have periodic orbits with a different number of unstable directions. We propose a new mechanism for the onset of unstable dimension variability based on an interior crisis, or a collision between a chaotic attractor and an unstable periodic orbit. We give a physical example by considering a high-dimensional dissipative physical system driven by impulsive periodic forcing

Attractors of magnetohydrodynamic flows in an Alfvenic state

Energy Technology Data Exchange (ETDEWEB)

Nunez, Manuel; Sanz, Javier [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)

1999-08-13

We present a simplified form of the magnetohydrodynamic system which describes the evolution of a plasma where the small-scale velocity and magnetic field are aligned in the form of Alfven waves, such as happens in several turbulent situations. Bounds on the dimension of the global attractor are found, and are shown to be an improvement of the standard ones for the full magnetohydrodynamic equations. (author)

Existence of global attractor for the Trojan Y Chromosome model

Directory of Open Access Journals (Sweden)

Xiaopeng Zhao

2012-04-01

Full Text Available This paper is concerned with the long time behavior of solution for the equation derived by the Trojan Y Chromosome (TYC model with spatial spread. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that this equations possesses a global attractor in $H^k(\\Omega^4$ $(k\\geq 0$ space.

Supersymmetric mechanics. Vol. 2. The attractor mechanism and space time singularities

International Nuclear Information System (INIS)

Bellucci, S.; Marrani, A.; Ferrara, S.

2006-01-01

This is the second volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. The first volume appears as Lect. Notes Physics, Vol. 698 ''Supersymmetric Mechanics, Vol.1: Supersymmetry, Noncommutativity and Matrix Models'' (2006) ISBN: 3-540-33313-4. The present extensive lecture supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. In such a framework, supersymmetry seems to be related to dynamical systems with fixed points, describing the equilibrium state and the stability features of the thermodynamics of black holes. After a qualitative overview, explicit examples realizing the attractor mechanism are treated at some length; they include relevant cases of asymptotically flat, maximal and non-maximal, extended supergravities in 4 and 5 dimensions. A number of recent advances along various directions of research on the attractor mechanism are also given. (orig.)

Anisotropic nonequilibrium hydrodynamic attractor

Science.gov (United States)

Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.

2018-02-01

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

Attractor comparisons based on density

International Nuclear Information System (INIS)

Carroll, T. L.

2015-01-01

Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling

The Lorentz Attractor and Other Attractors in the Economic System of a Firm

International Nuclear Information System (INIS)

Shapovalov, V I; Kazakov, N V

2015-01-01

A nonlinear model of the economic system of ''a firm'' is offered. It is shown that this model has several chaotic attractors, including the Lorentz attractor and a new attractor that, in our opinion, has not yet been described in the scientific literature. The chaotic nature of the attractors that were found was confirmed by computing the Lyapunov indicators. The functioning of our economic model is demonstrated with examples of firm behaviour that change the control parameters; these are well known in practice. In particular, it is shown that changes in the specific control parameters may change the system and avoid bankruptcy for the firm

Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls

Directory of Open Access Journals (Sweden)

Ciprian G. Gal

2006-11-01

Full Text Available In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem further. Using a Faedo-Galerkin method, we obtain the existence and uniqueness of a global solution to our problem, under more general assumptions than those in [7]. We then study its asymptotic behavior and prove the existence of an exponential attractor (and thus of a global attractor with finite dimension.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

Science.gov (United States)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Attractors for discrete periodic dynamical systems

Science.gov (United States)

John E. Franke; James F. Selgrade

2003-01-01

A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...

Attractor reconstruction for non-linear systems: a methodological note

Science.gov (United States)

Nichols, J.M.; Nichols, J.D.

2001-01-01

Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.

Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans.

Science.gov (United States)

Kalauzi, Aleksandar; Vuckovic, Aleksandra; Bojić, Tijana

2015-03-01

Organization of resting state cortical networks is of fundamental importance for the phenomenon of awareness, which is altered in the first part of hypnagogic period (Hori stages 1-4). Our aim was to investigate the change in brain topography pattern of EEG alpha attractor correlation dimension (CD) in the period of transition from Hori stage 1 to 4. EEG of ten healthy adult individuals was recorded in the wake and drowsy states, using a 14 channel average reference montage, from which 91 bipolar channels were derived and filtered in the wider alpha (6-14 Hz) range. Sixty 1s long epochs of each state and individual were subjected to CD calculation according to the Grassberger-Procaccia method. For such a collection of signals, two embedding dimensions, d={5, 10}, and 22 time delays τ=2-23 samples were explored. Optimal values were d=10 and τ=18, where both saturation and second zero crossing of the autocorrelation function occurred. Bipolar channel CD underwent a significant decrease during the transition and showed a positive linear correlation with electrode distance, stronger in the wake individuals. Topographic distribution of bipolar channels with above median CD changed from longitudinal anterior-posterior pattern (awake) to a more diagonal pattern, with localization in posterior regions (drowsiness). Our data are in line with the literature reporting functional segregation of neuronal assemblies in anterior and posterior regions during this transition. Our results should contribute to understanding of complex reorganization of the cortical part of alpha generators during the wake/drowsy transition. Copyright © 2014 Elsevier B.V. All rights reserved.

Horseshoes in modified Chen's attractors

International Nuclear Information System (INIS)

Huang Yan; Yang Xiaosong

2005-01-01

In this paper we study dynamics of a class of modified Chen's attractors, we show that these attractors are chaotic by giving a rigorous verification for existence of horseshoes in these systems. We prove that the Poincare maps derived from these modified Chen's attractors are semi-conjugate to the 2-shift map

Chaotic attractors with separated scrolls

International Nuclear Information System (INIS)

Bouallegue, Kais

2015-01-01

This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results

Generalized Attractor Points in Gauged Supergravity

Energy Technology Data Exchange (ETDEWEB)

Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Kallosh, Renata; /Stanford U., Phys. Dept.; Shmakova, Marina; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.

2011-08-15

The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schroedinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.

New estimates for human lung dimensions

International Nuclear Information System (INIS)

Kennedy, Christine; Sidavasan, Sivalal; Kramer, Gary

2008-01-01

Full text: The currently used lung dimensions in dosimetry were originally estimated in the 1940s from Army recruits. This study provides new estimates of lung dimensions based on images acquired from a sample from the general population (varying age and sex). Building accurate models, called phantoms, of the human lung requires that the spatial dimensions (length, width, and depth) be quantified, in addition to volume. Errors in dose estimates may result from improperly sized lungs as the counting efficiency of externally mounted detectors (e.g., in a lung counter) is dependent on the position of internally deposited radioactive material (i.e., the size of the lung). This study investigates the spatial dimensions of human lungs. Lung phantoms have previously been made in one of two sizes. The Lawrence Livermore National Laboratory Torso Phantom (LLNL) has deep, short lungs whose dimensions do not comply well with the data published in Report 23 (Reference Man) issued by the International Commission on Radiological Protection (ICRP). The Japanese Atomic Energy Research Institute Torso Phantom(JAERI), has longer, shallower lungs that also deviate from the ICRP values. However, careful examination of the ICRP recommended values shows that they are soft. In fact, they have been dropped from the ICRP's Report 89 which updates Report 23. Literature surveys have revealed a wealth of information on lung volume, but very little data on the spatial dimensions of human lungs. Better lung phantoms need to be constructed to more accurately represent a person so that dose estimates may be quantified more accurately in view of the new, lower, dose limits for occupationally exposed workers and the general public. Retrospective chest images of 60 patients who underwent imaging of the chest- lungs as part of their healthy persons occupational screening for lung disease were chosen. The chosen normal lung images represent the general population). Ages, gender and weight of the

Methodology of nuclear reactor monitoring and diagnostics using information dimension

International Nuclear Information System (INIS)

Suzudo, Tomoaki; Hayashi, Koji; Shinohara, Yoshikuni

1993-01-01

Reactor noise analysis method based on information dimension is applied to the monitoring and diagnosing of power oscillation. The method focuses on the utilization of the slope of the correlation integral (SOCI) which determines the information dimension of attractors. For practical application, the information dimension is expected to be the same as the fractal dimension of attractors; it can be used to classify different asymptotic regimes of nonlinear dynamical systems. We examined a real power oscillation using SOCI and the results implied that the oscillation was just a noisy limit cycle, although it is not possible to assert that there is no chaotic character in the oscillation because large oscillatory time-series data sets are not available. In addition, the application of SOCI to the real-time monitoring of power oscillation is proposed and examined. (author)

Attractor behaviour in ELKO cosmology

International Nuclear Information System (INIS)

Basak, Abhishek; Bhatt, Jitesh R.; Shankaranarayanan, S.; Varma, K.V. Prasantha

2013-01-01

We study the dynamics of ELKO in the context of accelerated phase of our universe. To avoid the fine tuning problem associated with the initial conditions, it is required that the dynamical equations lead to an early-time attractor. In the earlier works, it was shown that the dynamical equations containing ELKO fields do not lead to early-time stable fixed points. In this work, using redefinition of variables, we show that ELKO cosmology admits early-time stable fixed points. More interestingly, we show that ELKO cosmology admit two sets of attractor points corresponding to slow and fast-roll inflation. The fast-roll inflation attractor point is unique for ELKO as it is independent of the form of the potential. We also discuss the plausible choice of interaction terms in these two sets of attractor points and constraints on the coupling constant

On the Dynamics of a Model with Coexistence of Three Attractors: A Point, a Periodic Orbit and a Strange Attractor

Energy Technology Data Exchange (ETDEWEB)

Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Universitat Autònoma de Barcelona, Departament de Matemàtiques (Spain); Valls, Claudia, E-mail: cvalls@math.ist.utl.pt [Universidade de Lisboa, Departamento de Matemática, Instituto Superior Técnico (Portugal)

2017-06-15

For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals.

Black-Hole Attractors in N=1 Supergravity

CERN Document Server

Andrianopoli, L; Ferrara, Sergio; Trigiante, M; Andrianopoli, Laura; Auria, Riccardo D'; Ferrara, Sergio; Trigiante, Mario

2007-01-01

We study the attractor mechanism for N=1 supergravity coupled to vector and chiral multiplets and compute the attractor equations of these theories. These equations may have solutions depending on the choice of the holomorphic symmetric matrix f_{\\Lambda\\Sigma} which appears in the kinetic lagrangian of the vector sector. Models with non trivial electric-magnetic duality group which have or have not attractor behavior are exhibited. For a particular class of models, based on an N=1 reduction of homogeneous special geometries, the attractor equations are related to the theory of pure spinors.

Dynamic analysis, circuit implementation and passive control of a novel four-dimensional chaotic system with multiscroll attractor and multiple coexisting attractors

Science.gov (United States)

Lai, Bang-Cheng; He, Jian-Jun

2018-03-01

In this paper, we construct a novel 4D autonomous chaotic system with four cross-product nonlinear terms and five equilibria. The multiple coexisting attractors and the multiscroll attractor of the system are numerically investigated. Research results show that the system has various types of multiple attractors, including three strange attractors with a limit cycle, three limit cycles, two strange attractors with a pair of limit cycles, two coexisting strange attractors. By using the passive control theory, a controller is designed for controlling the chaos of the system. Both analytical and numerical studies verify that the designed controller can suppress chaotic motion and stabilise the system at the origin. Moreover, an electronic circuit is presented for implementing the chaotic system.

Determining the flexibility of regular and chaotic attractors

International Nuclear Information System (INIS)

Marhl, Marko; Perc, Matjaz

2006-01-01

We present an overview of measures that are appropriate for determining the flexibility of regular and chaotic attractors. In particular, we focus on those system properties that constitute its responses to external perturbations. We deploy a systematic approach, first introducing the simplest measure given by the local divergence of the system along the attractor, and then develop more rigorous mathematical tools for estimating the flexibility of the system's dynamics. The presented measures are tested on the regular Brusselator and chaotic Hindmarsh-Rose model of an excitable neuron with equal success, thus indicating the overall effectiveness and wide applicability range of the proposed theory. Since responses of dynamical systems to external signals are crucial in several scientific disciplines, and especially in natural sciences, we discuss several important aspects and biological implications of obtained results

Lifetime of chaotic attractors in a multidimensional laser system

International Nuclear Information System (INIS)

Pando L, C.L.; Cerdeira, H.A.

1995-01-01

We study the lifetimes of chaotic attractors at crises in a multidimensional laser system. This system describes the CO 2 laser with modulated losses and is known as the four-level model. The critical exponents which are related to the lifetimes of the attractors are estimated in terms of the corresponding eigenvalues and the measured characteristic lifetime in the model. The critical exponents in this model and those of its center manifold version are in good agreement. We conjecture that generically in the four-level model the critical exponents are close to 1/2 at crises. In addition, we compare predictions of a simpler and popular model known as the two-level model with those of the above mentioned models. (author). 21 refs, 2 figs, 3 tabs

Reconstruction of the El Nino attractor with neural networks

International Nuclear Information System (INIS)

Grieger, B.; Latif, M.

1993-01-01

Based on a combined data set of sea surface temperature, zonal surface wind stress and upper ocean heat content the dynamics of the El Nino phenomenon is investigated. In a reduced phase space spanned by the first four EOFs two different stochastic models are estimated from the data. A nonlinear model represented by a simulated neural network is compared with a linear model obtained with the Principal Oscillation Pattern (POP) analysis. While the linear model is limited to damped oscillations onto a fix point attractor, the nonlinear model recovers a limit cycle attractor. This indicates that the real system is located above the bifurcation point in parameter space supporting self-sustained oscillations. The results are discussed with respect to consistency with current theory. (orig.)

Cosmological attractors in massive gravity

CERN Document Server

Dubovsky, S; Tkachev, I I

2005-01-01

We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra ``confining'' term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.

Correlation Dimension Estimation for Classification

Czech Academy of Sciences Publication Activity Database

Jiřina, Marcel; Jiřina jr., M.

2006-01-01

Roč. 1, č. 3 (2006), s. 547-557 ISSN 1895-8648 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : correlation dimension * probability density estimation * classification * UCI MLR Subject RIV: BA - General Mathematics

Applying Chaos Theory to Careers: Attraction and Attractors

Science.gov (United States)

Pryor, Robert G. L.; Bright, Jim E. H.

2007-01-01

This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

Science.gov (United States)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2018-02-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

概率密度函数法研究重构吸引子的结构%Probability Density Function Method for Observing Reconstructed Attractor Structure

Institute of Scientific and Technical Information of China (English)

陆宏伟; 陈亚珠; 卫青

2004-01-01

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men.PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor.To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure.Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems.It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough.A cluster effect mechanism is presented to explain this phenomenon.By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated.Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

Cusps enable line attractors for neural computation

International Nuclear Information System (INIS)

Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis

2017-01-01

Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

Cusps enable line attractors for neural computation

Science.gov (United States)

Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis

2017-11-01

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

Attractors in complex networks

Science.gov (United States)

Rodrigues, Alexandre A. P.

2017-10-01

In the framework of the generalized Lotka-Volterra model, solutions representing multispecies sequential competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic channel" forms part of an attractor. We prove that, generically, in an attracting heteroclinic network involving a finite number of hyperbolic and non-resonant saddle-equilibria whose linearization has only real eigenvalues, the connections corresponding to the most positive expanding eigenvalues form part of an attractor (observable in numerical simulations).

Moduli Backreaction on Inflationary Attractors

CERN Document Server

Roest, Diederik; Werkman, Pelle

2016-01-01

We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.

Counting and classifying attractors in high dimensional dynamical systems.

Science.gov (United States)

Bagley, R J; Glass, L

1996-12-07

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

Non-linguistic Conditions for Causativization as a Linguistic Attractor

OpenAIRE

Johanna Nichols; Johanna Nichols; Johanna Nichols

2018-01-01

An attractor, in complex systems theory, is any state that is more easily or more often entered or acquired than departed or lost; attractor states therefore accumulate more members than non-attractors, other things being equal. In the context of language evolution, linguistic attractors include sounds, forms, and grammatical structures that are prone to be selected when sociolinguistics and language contact make it possible for speakers to choose between competing forms. The reasons why an e...

Revisiting non-Gaussianity from non-attractor inflation models

Science.gov (United States)

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

2018-05-01

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

Fibre inflation and α-attractors

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata; Linde, Andrei [Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; Leiden Univ. (Netherlands). Lorentz Inst. for Theoretical Physics; Roest, Diederik [Groningen Univ. (Netherlands). Van Swinderen Inst. for Particle Physics and Gravity; Westphal, Alexander [DESY, Hamburg (Germany). Theory Group; Yamada, Yusuke [Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics

2017-07-15

Fibre inflation is a specific string theory construction based on the Large Volume Scenario that produces an inflationary plateau. We outline its relation to α-attractor models for inflation, with the cosmological sector originating from certain string theory corrections leading to α=2 and α=1/2. Above a certain field range, the steepening effect of higher-order corrections leads first to the breakdown of single-field slow-roll and after that to the onset of 2-field dynamics: the overall volume of the extra dimensions starts to participate in the effective dynamics. Finally, we propose effective supergravity models of fibre inflation based on an D3 uplift term with a nilpotent superfield. Specific moduli dependent D3 induced geometries lead to cosmological fibre models but have in addition a de Sitter minimum exit. These supergravity models motivated by fibre inflation are relatively simple, stabilize the axions and disentangle the Hubble parameter from supersymmetry breaking.

Fibre inflation and α-attractors

Science.gov (United States)

Kallosh, Renata; Linde, Andrei; Roest, Diederik; Westphal, Alexander; Yamada, Yusuke

2018-02-01

Fibre inflation is a specific string theory construction based on the Large Volume Scenario that produces an inflationary plateau. We outline its relation to α-attractor models for inflation, with the cosmological sector originating from certain string theory corrections leading to α = 2 and α = 1/2. Above a certain field range, the steepening effect of higher-order corrections leads first to the breakdown of single-field slow-roll and after that to the onset of 2-field dynamics: the overall volume of the extra dimensions starts to participate in the effective dynamics. Finally, we propose effective supergravity models of fibre inflation based on an \\overline{D3} uplift term with a nilpotent superfield. Specific moduli dependent \\overline{D3} induced geometries lead to cosmological fibre models but have in addition a de Sitter minimum exit. These supergravity models motivated by fibre inflation are relatively simple, stabilize the axions and disentangle the Hubble parameter from supersymmetry breaking.

β-expansion attractors observed in A/D converters

Science.gov (United States)

Kohda, Tohru; Horio, Yoshihiko; Aihara, Kazuyuki

2012-12-01

The recently proposed β-encoders, analog-to-digital converters using an amplifier with a factor β and a flaky quantizer with threshold ν, have proven to be explained by the deterministic dynamics of multi-valued Rényi-Parry maps. Such a map is locally eventually onto [ν-1, ν), which is topologically conjugate to Parry's (β,α)-map with α =(β-1)(ν-1). This implies that β-encoders have a closed subinterval [ν-1,ν), which includes an attractor. Thus, the iteration of the multi-valued Rényi-Parry map performs the β-expansion of x while quantization errors in β-encoders behave chaotically and do not converge to a fixed point. This β-expansion attractor is relatively simpler than previously reported attractors. The object of this paper is twofold: to observe the embedded attractors in the β-encoder and to identify attractors that are useful for spread-spectrum codes and optimization techniques using pseudo-random numbers.

Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

OpenAIRE

You, Bo; Li, Fang

2016-01-01

This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere...

Moduli backreaction on inflationary attractors

International Nuclear Information System (INIS)

Roest, Diederik; Werkman, Pelle

2016-07-01

We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT- scenario and cosmological α-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for α-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.

When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

International Nuclear Information System (INIS)

Pan, Indranil; Das, Saptarshi

2015-01-01

Highlights: •New 3D continuous time chaotic systems with analytical expressions are obtained. •The multi-gene genetic programming (MGGP) paradigm is employed to achieve this. •Extends earlier works for evolving generalised family of Lorenz attractors. •Over one hundred of new chaotic attractors along with their parameters are reported. •The MGGP method have the potential for finding other similar chaotic attractors. -- Abstract: In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone

COSMOS-e'-soft Higgsotic attractors

Science.gov (United States)

Choudhury, Sayantan

2017-07-01

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R^2 gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δ N formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

COSMOS-e"'-soft Higgsotic attractors

International Nuclear Information System (INIS)

Choudhury, Sayantan

2017-01-01

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R"2 gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δN formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness. (orig.)

Tetrapterous butterfly attractors in modified Lorenz systems

International Nuclear Information System (INIS)

Yu Simin; Tang, Wallace K.S.

2009-01-01

In this paper, the Lorenz-type tetrapterous butterfly attractors are firstly reported. With the introduction of multiple segment piecewise linear functions, these interesting and complex attractors are obtained from two different modified Lorenz models. This approach are verified in both simulations and experiments.

Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

Energy Technology Data Exchange (ETDEWEB)

Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)

2014-07-04

To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.

A birational mapping with a strange attractor: post-critical set and covariant curves

International Nuclear Information System (INIS)

Bouamra, M; Hassani, S; Maillard, J-M

2009-01-01

We consider some two-dimensional birational transformations. One of them is a birational deformation of the Henon map. For some of these birational mappings, the post-critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic 2-form. One may also have an infinite post-critical set yielding a covariant curve which is not algebraic (transcendental). For two of the birational mappings considered, the post-critical set is finite and we claim that there is no algebraic covariant curve and no preserved meromorphic 2-form. For these two mappings with finite post-critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.

Attractors under discretisation

CERN Document Server

Han, Xiaoying

2017-01-01

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.

Attractors and basins of dynamical systems

Directory of Open Access Journals (Sweden)

Attila Dénes

2011-03-01

Full Text Available There are several programs for studying dynamical systems, but none of them is very useful for investigating basins and attractors of higher dimensional systems. Our goal in this paper is to show a new algorithm for finding even chaotic attractors and their basins for these systems. We present an implementation and examples for the use of this program.

Multi-wing hyperchaotic attractors from coupled Lorenz systems

International Nuclear Information System (INIS)

Grassi, Giuseppe; Severance, Frank L.; Miller, Damon A.

2009-01-01

This paper illustrates an approach to generate multi-wing attractors in coupled Lorenz systems. In particular, novel four-wing (eight-wing) hyperchaotic attractors are generated by coupling two (three) identical Lorenz systems. The paper shows that the equilibria of the proposed systems have certain symmetries with respect to specific coordinate planes and the eigenvalues of the associated Jacobian matrices exhibit the property of similarity. In analogy with the original Lorenz system, where the two-wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four-wings (eight-wings) of these attractors are located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues.

Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

Science.gov (United States)

Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

2018-06-01

We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

Supersymmetry and attractors

International Nuclear Information System (INIS)

Ferrara, S.; Kallosh, R.

1996-01-01

We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the Bertotti-Robinson-type geometry. These results provide an explicit model-independent expression for the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropy-area formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge. copyright 1996 The American Physical Society

A Novel Image Encryption Scheme Based on Clifford Attractor and Noisy Logistic Map for Secure Transferring Images in Navy

Directory of Open Access Journals (Sweden)

Mohadeseh Kanafchian

2017-04-01

In this paper, we first give a brief introduction into chaotic image encryption and then we investigate some important properties and behaviour of the logistic map. The logistic map, aperiodic trajectory, or random-like fluctuation, could not be obtained with some choice of initial condition. Therefore, a noisy logistic map with an additive system noise is introduced. The proposed scheme is based on the extended map of the Clifford strange attractor, where each dimension has a specific role in the encryption process. Two dimensions are used for pixel permutation and the third dimension is used for pixel diffusion. In order to optimize the Clifford encryption system we increase the space key by using the noisy logistic map and a novel encryption scheme based on the Clifford attractor and the noisy logistic map for secure transfer images is proposed. This algorithm consists of two parts: the noisy logistic map shuffle of the pixel position and the pixel value. We use times for shuffling the pixel position and value then we generate the new pixel position and value by the Clifford system. To illustrate the efficiency of the proposed scheme, various types of security analysis are tested. It can be concluded that the proposed image encryption system is a suitable choice for practical applications.

Internal Waves and Wave Attractors in Enceladus' Subsurface Ocean

Science.gov (United States)

van Oers, A. M.; Maas, L. R.; Vermeersen, B. L. A.

2016-12-01

One of the most peculiar features on Saturn moon Enceladus is its so-called tiger stripe pattern at the geologically active South Polar Terrain (SPT), as first observed in detail by the Cassini spacecraft early 2005. It is generally assumed that the four almost parallel surface lines that constitute this pattern are faults in the icy surface overlying a confined salty water reservoir. In 2013, we formulated the original idea [Vermeersen et al., AGU Fall Meeting 2013, abstract #P53B-1848] that the tiger stripe pattern is formed and maintained by induced, tidally and rotationally driven, wave-attractor motions in the ocean underneath the icy surface of the tiger-stripe region. Such wave-attractor motions are observed in water tank experiments in laboratories on Earth and in numerical experiments [Maas et al., Nature, 338, 557-561, 1997; Drijfhout and Maas, J. Phys. Oceanogr., 37, 2740-2763, 2007; Hazewinkel et al., Phys. Fluids, 22, 107102, 2010]. Numerical simulations show the persistence of wave attractors for a range of ocean shapes and stratifications. The intensification of the wave field near the location of the surface reflections of wave attractors has been numerically and experimentally confirmed. We measured the forces a wave attractor exerts on a solid surface, near a reflection point. These reflection points would correspond to the location of the tiger stripes. Combining experiments and numerical simulations we conclude that (1) wave attractors can exist in Enceladus' subsurface sea, (2) their shape can be matched to the tiger stripes, (3) the wave attractors cause a localized force at the water-ice boundaries, (4) this force could have been large enough to contribute to fracturing the ice and (5) the wave attractors localize energy (and particles) and cause dissipation along its path, helping explain Enceladus' enigmatic heat output at the tiger stripes.

Hyperbolic Plykin attractor can exist in neuron models

DEFF Research Database (Denmark)

Belykh, V.; Belykh, I.; Mosekilde, Erik

2005-01-01

Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...

Strange Attractors in Drift Wave Turbulence

International Nuclear Information System (INIS)

Lewandowski, J.L.V.

2003-01-01

A multi-grid part-in-cell algorithm for a shearless slab drift wave model with kinetic electrons is presented. The algorithm, which is based on an exact separation of adiabatic and nonadiabatic electron responses, is used to investigate the presence of strange attractors in drift wave turbulence. Although the simulation model has a large number of degrees of freedom, it is found that the strange attractor is low-dimensional and that it is strongly affected by dissipative (collisional) effects

Attractor neural networks with resource-efficient synaptic connectivity

Science.gov (United States)

Pehlevan, Cengiz; Sengupta, Anirvan

Memories are thought to be stored in the attractor states of recurrent neural networks. Here we explore how resource constraints interplay with memory storage function to shape synaptic connectivity of attractor networks. We propose that given a set of memories, in the form of population activity patterns, the neural circuit choses a synaptic connectivity configuration that minimizes a resource usage cost. We argue that the total synaptic weight (l1-norm) in the network measures the resource cost because synaptic weight is correlated with synaptic volume, which is a limited resource, and is proportional to neurotransmitter release and post-synaptic current, both of which cost energy. Using numerical simulations and replica theory, we characterize optimal connectivity profiles in resource-efficient attractor networks. Our theory explains several experimental observations on cortical connectivity profiles, 1) connectivity is sparse, because synapses are costly, 2) bidirectional connections are overrepresented and 3) are stronger, because attractor states need strong recurrence.

Non-linguistic Conditions for Causativization as a Linguistic Attractor.

Science.gov (United States)

Nichols, Johanna

2017-01-01

An attractor, in complex systems theory, is any state that is more easily or more often entered or acquired than departed or lost; attractor states therefore accumulate more members than non-attractors, other things being equal. In the context of language evolution, linguistic attractors include sounds, forms, and grammatical structures that are prone to be selected when sociolinguistics and language contact make it possible for speakers to choose between competing forms. The reasons why an element is an attractor are linguistic (auditory salience, ease of processing, paradigm structure, etc.), but the factors that make selection possible and propagate selected items through the speech community are non-linguistic. This paper uses the consonants in personal pronouns to show what makes for an attractor and how selection and diffusion work, then presents a survey of several language families and areas showing that the derivational morphology of pairs of verbs like fear and frighten , or Turkish korkmak 'fear, be afraid' and korkutmak 'frighten, scare', or Finnish istua 'sit' and istutta 'seat (someone)', or Spanish sentarse 'sit down' and sentar 'seat (someone)' is susceptible to selection. Specifically, the Turkish and Finnish pattern, where 'seat' is derived from 'sit' by addition of a suffix-is an attractor and a favored target of selection. This selection occurs chiefly in sociolinguistic contexts of what is defined here as linguistic symbiosis, where languages mingle in speech, which in turn is favored by certain demographic, sociocultural, and environmental factors here termed frontier conditions. Evidence is surveyed from northern Eurasia, the Caucasus, North and Central America, and the Pacific and from both modern and ancient languages to raise the hypothesis that frontier conditions and symbiosis favor causativization.

An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

Science.gov (United States)

Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei

2013-01-01

Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems. Availability The software package is available at https://sites.google.com/site/desheng619/download. PMID:23585840

Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

Science.gov (United States)

Sone, Akira; Cappellaro, Paola

2017-12-01

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.

Tornado intensity estimated from damage path dimensions.

Science.gov (United States)

Elsner, James B; Jagger, Thomas H; Elsner, Ian J

2014-01-01

The Newcastle/Moore and El Reno tornadoes of May 2013 are recent reminders of the destructive power of tornadoes. A direct estimate of a tornado's power is difficult and dangerous to get. An indirect estimate on a categorical scale is available from a post-storm survery of the damage. Wind speed bounds are attached to the scale, but the scale is not adequate for analyzing trends in tornado intensity separate from trends in tornado frequency. Here tornado intensity on a continuum is estimated from damage path length and width, which are measured on continuous scales and correlated to the EF rating. The wind speeds on the EF scale are treated as interval censored data and regressed onto the path dimensions and fatalities. The regression model indicates a 25% increase in expected intensity over a threshold intensity of 29 m s(-1) for a 100 km increase in path length and a 17% increase in expected intensity for a one km increase in path width. The model shows a 43% increase in the expected intensity when fatalities are observed controlling for path dimensions. The estimated wind speeds correlate at a level of .77 (.34, .93) [95% confidence interval] with a small sample of wind speeds estimated independently from a doppler radar calibration. The estimated wind speeds allow analyses to be done on the tornado database that are not possible with the categorical scale. The modeled intensities can be used in climatology and in environmental and engineering applications. Research is needed to understand the upward trends in path length and width.

Tornado intensity estimated from damage path dimensions.

Directory of Open Access Journals (Sweden)

James B Elsner

Full Text Available The Newcastle/Moore and El Reno tornadoes of May 2013 are recent reminders of the destructive power of tornadoes. A direct estimate of a tornado's power is difficult and dangerous to get. An indirect estimate on a categorical scale is available from a post-storm survery of the damage. Wind speed bounds are attached to the scale, but the scale is not adequate for analyzing trends in tornado intensity separate from trends in tornado frequency. Here tornado intensity on a continuum is estimated from damage path length and width, which are measured on continuous scales and correlated to the EF rating. The wind speeds on the EF scale are treated as interval censored data and regressed onto the path dimensions and fatalities. The regression model indicates a 25% increase in expected intensity over a threshold intensity of 29 m s(-1 for a 100 km increase in path length and a 17% increase in expected intensity for a one km increase in path width. The model shows a 43% increase in the expected intensity when fatalities are observed controlling for path dimensions. The estimated wind speeds correlate at a level of .77 (.34, .93 [95% confidence interval] with a small sample of wind speeds estimated independently from a doppler radar calibration. The estimated wind speeds allow analyses to be done on the tornado database that are not possible with the categorical scale. The modeled intensities can be used in climatology and in environmental and engineering applications. Research is needed to understand the upward trends in path length and width.

Generation of multi-wing chaotic attractor in fractional order system

International Nuclear Information System (INIS)

Zhang Chaoxia; Yu Simin

2011-01-01

Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

Non-linguistic Conditions for Causativization as a Linguistic Attractor

Directory of Open Access Journals (Sweden)

Johanna Nichols

2018-01-01

Full Text Available An attractor, in complex systems theory, is any state that is more easily or more often entered or acquired than departed or lost; attractor states therefore accumulate more members than non-attractors, other things being equal. In the context of language evolution, linguistic attractors include sounds, forms, and grammatical structures that are prone to be selected when sociolinguistics and language contact make it possible for speakers to choose between competing forms. The reasons why an element is an attractor are linguistic (auditory salience, ease of processing, paradigm structure, etc., but the factors that make selection possible and propagate selected items through the speech community are non-linguistic. This paper uses the consonants in personal pronouns to show what makes for an attractor and how selection and diffusion work, then presents a survey of several language families and areas showing that the derivational morphology of pairs of verbs like fear and frighten, or Turkish korkmak ‘fear, be afraid’ and korkutmak ‘frighten, scare’, or Finnish istua ‘sit’ and istutta ‘seat (someone’, or Spanish sentarse ‘sit down’ and sentar ‘seat (someone’ is susceptible to selection. Specifically, the Turkish and Finnish pattern, where ‘seat’ is derived from ‘sit’ by addition of a suffix—is an attractor and a favored target of selection. This selection occurs chiefly in sociolinguistic contexts of what is defined here as linguistic symbiosis, where languages mingle in speech, which in turn is favored by certain demographic, sociocultural, and environmental factors here termed frontier conditions. Evidence is surveyed from northern Eurasia, the Caucasus, North and Central America, and the Pacific and from both modern and ancient languages to raise the hypothesis that frontier conditions and symbiosis favor causativization.

Connecting coherent structures and strange attractors

Science.gov (United States)

Keefe, Laurence R.

1990-01-01

A concept of turbulence derived from nonlinear dynamical systems theory suggests that turbulent solutions to the Navier-Stokes equations are restricted to strange attractors, and, by implication, that turbulent phenomenology must find some expression or source in the structure of these mathematical objects. Examples and discussions are presented to link coherent structures to some of the commonly known characteristics of strange attractors. Basic to this link is a geometric interpretation of conditional sampling techniques employed to educe coherent structures that offers an explanation for their appearance in measurements as well as their size.

Attractors of equations of non-Newtonian fluid dynamics

International Nuclear Information System (INIS)

Zvyagin, V G; Kondrat'ev, S K

2014-01-01

This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles

Coexisting chaotic attractors in a single neuron model with adapting feedback synapse

International Nuclear Information System (INIS)

Li Chunguang; Chen Guanrong

2005-01-01

In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra

Attractors near grazing–sliding bifurcations

International Nuclear Information System (INIS)

Glendinning, P; Kowalczyk, P; Nordmark, A B

2012-01-01

In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist

Sneutrino Inflation with $\\alpha$-attractors

CERN Document Server

Kallosh, Renata; Roest, Diederik; Wrase, Timm

2016-11-22

Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. A crucial ingredient in existing constructions for sneutrino (multi-)natural inflation is an unbroken discrete shift symmetry. We demonstrate that a similar construction applies to $\\alpha$-attractor models. In this case the hyperbolic geometry protects the neutrino Yukawa couplings to the inflaton field, and the masses of leptons and Higgs fields, from blowing up when the inflaton is super-Planckian. We find that the predictions for $n_s$ and $r$ for $\\alpha$-attractor cosmological models, compatible with the current cosmological data, are preserved in the presence of the neutrino sector.

Application of fixed point theory to chaotic attractors of forced oscillators

International Nuclear Information System (INIS)

Stewart, H.B.

1990-11-01

A review of the structure of chaotic attractors of periodically forced second order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand. (author)

The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations

Energy Technology Data Exchange (ETDEWEB)

Simpson, D.J.W., E-mail: d.j.w.simpson@massey.ac.nz

2016-09-07

An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical evidence is provided to show that this invariant set can be chaotic. The transition occurs locally (in a neighbourhood of a point) and instantaneously (for a single critical parameter value). This phenomenon is illustrated for the normal form of a boundary equilibrium bifurcation in three dimensions using parameter values adapted from of a piecewise-linear model of a chaotic electrical circuit. The variation of a secondary parameter reveals a period-doubling cascade to chaos with windows of periodicity. The dynamics is well approximated by a one-dimensional unimodal map which explains the bifurcation structure. The robustness of the attractor is also investigated by studying the influence of nonlinear terms. - Highlights: • A boundary equilibrium bifurcation involving stable and saddle foci is considered. • A two-dimensional return map is constructed and approximated by a one-dimensional map. • A trapping region and Smale horseshoe are identified for a Rössler-like attractor. • Bifurcation diagrams reveal period-doubling cascades and windows of periodicity.

COSMOS-e{sup '}-soft Higgsotic attractors

Energy Technology Data Exchange (ETDEWEB)

Choudhury, Sayantan [Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India)

2017-07-15

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R{sup 2} gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δN formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness. (orig.)

Closed contour fractal dimension estimation by the Fourier transform

International Nuclear Information System (INIS)

Florindo, J.B.; Bruno, O.M.

2011-01-01

Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

Context-dependent retrieval of information by neural-network dynamics with continuous attractors.

Science.gov (United States)

Tsuboshita, Yukihiro; Okamoto, Hiroshi

2007-08-01

Memory retrieval in neural networks has traditionally been described by dynamic systems with discrete attractors. However, recent neurophysiological findings of graded persistent activity suggest that memory retrieval in the brain is more likely to be described by dynamic systems with continuous attractors. To explore what sort of information processing is achieved by continuous-attractor dynamics, keyword extraction from documents by a network of bistable neurons, which gives robust continuous attractors, is examined. Given an associative network of terms, a continuous attractor led by propagation of neuronal activation in this network appears to represent keywords that express underlying meaning of a document encoded in the initial state of the network-activation pattern. A dominant hypothesis in cognitive psychology is that long-term memory is archived in the network structure, which resembles associative networks of terms. Our results suggest that keyword extraction by the neural-network dynamics with continuous attractors might symbolically represent context-dependent retrieval of short-term memory from long-term memory in the brain.

Noise-induced attractor annihilation in the delayed feedback logistic map

International Nuclear Information System (INIS)

Pisarchik, A.N.; Martínez-Zérega, B.E.

2013-01-01

We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

Science.gov (United States)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Measuring surface topography by scanning electron microscopy. II. Analysis of three estimators of surface roughness in second dimension and third dimension.

Science.gov (United States)

Bonetto, Rita Dominga; Ladaga, Juan Luis; Ponz, Ezequiel

2006-04-01

Scanning electron microscopy (SEM) is widely used in surface studies and continuous efforts are carried out in the search of estimators of different surface characteristics. By using the variogram, we developed two of these estimators that were used to characterize the surface roughness from the SEM image texture. One of the estimators is related to the crossover between fractal region at low scale and the periodic region at high scale, whereas the other estimator characterizes the periodic region. In this work, a full study of these estimators and the fractal dimension in two dimensions (2D) and three dimensions (3D) was carried out for emery papers. We show that the obtained fractal dimension with only one image is good enough to characterize the roughness surface because its behavior is similar to those obtained with 3D height data. We show also that the estimator that indicates the crossover is related to the minimum cell size in 2D and to the average particle size in 3D. The other estimator has different values for the three studied emery papers in 2D but it does not have a clear meaning, and these values are similar for those studied samples in 3D. Nevertheless, it indicates the formation tendency of compound cells. The fractal dimension values from the variogram and from an area versus step log-log graph were studied with 3D data. Both methods yield different values corresponding to different information from the samples.

Complicated basins and the phenomenon of amplitude death in coupled hidden attractors

Energy Technology Data Exchange (ETDEWEB)

Chaudhuri, Ushnish [Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi 110021 (India); Department of Physics, National University of Singapore, Singapore 117551 (Singapore); Prasad, Awadhesh, E-mail: awadhesh@physics.du.ac.in [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India)

2014-02-07

Understanding hidden attractors, whose basins of attraction do not contain the neighborhood of equilibrium of the system, are important in many physical applications. We observe riddled-like complicated basins of coexisting hidden attractors both in coupled and uncoupled systems. Amplitude death is observed in coupled hidden attractors with no fixed point using nonlinear interaction. A new route to amplitude death is observed in time-delay coupled hidden attractors. Numerical results are presented for systems with no or one stable fixed point. The applications are highlighted.

Synchronization in Coupled Oscillators with Two Coexisting Attractors

International Nuclear Information System (INIS)

Han-Han, Zhu; Jun-Zhong, Yang

2008-01-01

Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Duffing oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions. (general)

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

International Nuclear Information System (INIS)

Hong-Yan, Jia; Zeng-Qiang, Chen; Zhu-Zhi, Yuan

2010-01-01

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation. (general)

Describing chaotic attractors: Regular and perpetual points

Science.gov (United States)

Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz

2018-03-01

We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.

Generating two simultaneously chaotic attractors with a switching piecewise-linear controller

International Nuclear Information System (INIS)

Zheng Zuohuan; Lue Jinhu; Chen Guanrong; Zhou Tianshou; Zhang Suochun

2004-01-01

It has been demonstrated that a piecewise-linear system can generate chaos under suitable conditions. This paper proposes a novel method for simultaneously creating two symmetrical chaotic attractor--an upper-attractor and a lower-attractor--in a 3D linear autonomous system. Basically dynamical behaviors of this new chaotic system are further investigated. Especially, the chaos formation mechanism is explored by analyzing the structure of fixed points and the system trajectories

Sparse Array Angle Estimation Using Reduced-Dimension ESPRIT-MUSIC in MIMO Radar

Directory of Open Access Journals (Sweden)

Chaozhu Zhang

2013-01-01

Full Text Available Sparse linear arrays provide better performance than the filled linear arrays in terms of angle estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. In this paper, both the transmit array and receive array are sparse linear arrays in the bistatic MIMO radar. Firstly, we present an ESPRIT-MUSIC method in which ESPRIT algorithm is used to obtain ambiguous angle estimates. The disambiguation algorithm uses MUSIC-based procedure to identify the true direction cosine estimate from a set of ambiguous candidate estimates. The paired transmit angle and receive angle can be estimated and the manifold ambiguity can be solved. However, the proposed algorithm has high computational complexity due to the requirement of two-dimension search. Further, the Reduced-Dimension ESPRIT-MUSIC (RD-ESPRIT-MUSIC is proposed to reduce the complexity of the algorithm. And the RD-ESPRIT-MUSIC only demands one-dimension search. Simulation results demonstrate the effectiveness of the method.

Sparse array angle estimation using reduced-dimension ESPRIT-MUSIC in MIMO radar.

Science.gov (United States)

Zhang, Chaozhu; Pang, Yucai

2013-01-01

Sparse linear arrays provide better performance than the filled linear arrays in terms of angle estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. In this paper, both the transmit array and receive array are sparse linear arrays in the bistatic MIMO radar. Firstly, we present an ESPRIT-MUSIC method in which ESPRIT algorithm is used to obtain ambiguous angle estimates. The disambiguation algorithm uses MUSIC-based procedure to identify the true direction cosine estimate from a set of ambiguous candidate estimates. The paired transmit angle and receive angle can be estimated and the manifold ambiguity can be solved. However, the proposed algorithm has high computational complexity due to the requirement of two-dimension search. Further, the Reduced-Dimension ESPRIT-MUSIC (RD-ESPRIT-MUSIC) is proposed to reduce the complexity of the algorithm. And the RD-ESPRIT-MUSIC only demands one-dimension search. Simulation results demonstrate the effectiveness of the method.

Trajectory attractors of equations of mathematical physics

International Nuclear Information System (INIS)

Vishik, Marko I; Chepyzhov, Vladimir V

2011-01-01

In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

Controlling Strange Attractor in Dynamics

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

A nonlinear system which exhibits a strange attractor is considered, with the goal of illustrating how to control the chaotic dynamical system and to obtain a desired attracting periodic orbit by the OGY control algorithm.

Attractors for a class of doubly nonlinear parabolic systems

Directory of Open Access Journals (Sweden)

Hamid El Ouardi

2006-03-01

Full Text Available In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\\left[ L^{\\infty }(\\Omega \\right] ^{2}$ and ${\\prod_{i=1}^{2}}{B_{\\infty }^{1+\\sigma_{i},p_{i}}( \\Omega } $.

[Extraction and recognition of attractors in three-dimensional Lorenz plot].

Science.gov (United States)

Hu, Min; Jang, Chengfan; Wang, Suxia

2018-02-01

Lorenz plot (LP) method which gives a global view of long-time electrocardiogram signals, is an efficient simple visualization tool to analyze cardiac arrhythmias, and the morphologies and positions of the extracted attractors may reveal the underlying mechanisms of the onset and termination of arrhythmias. But automatic diagnosis is still impossible because it is lack of the method of extracting attractors by now. We presented here a methodology of attractor extraction and recognition based upon homogeneously statistical properties of the location parameters of scatter points in three dimensional LP (3DLP), which was constructed by three successive RR intervals as X , Y and Z axis in Cartesian coordinate system. Validation experiments were tested in a group of RR-interval time series and tags data with frequent unifocal premature complexes exported from a 24-hour Holter system. The results showed that this method had excellent effective not only on extraction of attractors, but also on automatic recognition of attractors by the location parameters such as the azimuth of the points peak frequency ( A PF ) of eccentric attractors once stereographic projection of 3DLP along the space diagonal. Besides, A PF was still a powerful index of differential diagnosis of atrial and ventricular extrasystole. Additional experiments proved that this method was also available on several other arrhythmias. Moreover, there were extremely relevant relationships between 3DLP and two dimensional LPs which indicate any conventional achievement of LPs could be implanted into 3DLP. It would have a broad application prospect to integrate this method into conventional long-time electrocardiogram monitoring and analysis system.

Existence of a new three-dimensional chaotic attractor

International Nuclear Information System (INIS)

Wang Jiezhi; Chen Zengqiang; Yuan Zhuzhi

2009-01-01

In this paper, one heteroclinic orbit of a new three-dimensional continuous autonomous chaotic system, whose chaotic attractor belongs to the conjugate Lue attractor, is found. The series expression of the heteroclinic orbit of Shil'nikov type is derived by using the undetermined coefficient method. The uniform convergence of the precise series expansions of this heteroclinic orbits is proved. According to the Shil'nikov theorem, this system clearly has Smale horseshoes and the horseshoe chaos.

Global dynamics of a reaction-diffusion system

Directory of Open Access Journals (Sweden)

Yuncheng You

2011-02-01

Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.

Cortical computations via transient attractors.

Science.gov (United States)

Rourke, Oliver L C; Butts, Daniel A

2017-01-01

The ability of sensory networks to transiently store information on the scale of seconds can confer many advantages in processing time-varying stimuli. How a network could store information on such intermediate time scales, between typical neurophysiological time scales and those of long-term memory, is typically attributed to persistent neural activity. An alternative mechanism which might allow for such information storage is through temporary modifications to the neural connectivity which decay on the same second-long time scale as the underlying memories. Earlier work that has explored this method has done so by emphasizing one attractor from a limited, pre-defined set. Here, we describe an alternative, a Transient Attractor network, which can learn any pattern presented to it, store several simultaneously, and robustly recall them on demand using targeted probes in a manner reminiscent of Hopfield networks. We hypothesize that such functionality could be usefully embedded within sensory cortex, and allow for a flexibly-gated short-term memory, as well as conferring the ability of the network to perform automatic de-noising, and separation of input signals into distinct perceptual objects. We demonstrate that the stored information can be refreshed to extend storage time, is not sensitive to noise in the system, and can be turned on or off by simple neuromodulation. The diverse capabilities of transient attractors, as well as their resemblance to many features observed in sensory cortex, suggest the possibility that their actions might underlie neural processing in many sensory areas.

The power spectrum of inflationary attractors

International Nuclear Information System (INIS)

Broy, Benedict J.; Westphal, Alexander; Roest, Diederik

2014-08-01

Inflationary attractors predict the spectral index and tensor-to-scalar ratio to take specific values that are consistent with Planck. An example is the universal attractor for models with a generalised non-minimal coupling, leading to Starobinsky inflation. In this letter we demonstrate that it also predicts a specific relation between the amplitude of the power spectrum and the number of e-folds. The length and height of the inflationary plateau are related via the non-minimal coupling: in a wide variety of examples, the observed power normalisation leads to at least 55 flat e-foldings. Prior to this phase, the inflationary predictions vary and can account for the observational indications of power loss at large angular scales.

Age, Sex and Stature Estimation from Footprint Dimensions

Directory of Open Access Journals (Sweden)

Paurbhi Singh

2017-04-01

Full Text Available Objectives: The present study was carried out to evaluate the utility and reliability of footprint dimensions in age, sex and stature determination in the North Indian population. Materials and Methods: This study was carried out using a sample of 400 people (146 female and 254 male aged 10-65 years in Uttar Pradesh, North Western state of India. Footprints of both feet were taken bilaterally, and thus a total of 800 prints were obtained. A cluster of 7 measurements were taken carefully with the help of a scientific scale ruler. Five measurements were length dimensions from the most anterior part of the toe (T1–T5 to the mid rear heel point and two were breadth dimensions from both left and right footprints: breadth at ball (BBAL, breadth at heel (BHEL and 2 indexes: heel-ball Index (HBI and footprint index (FPI. All data were analyzed statistically using Student’s t-test, regression coefficient and Pearson’s correlation for the estimation of sex on the basis of footprint dimensions. Results: The T1 in left footprints was greater than right footprints in males, while T1 and BBAL were both found to be greater in left footprints than right footprints in females. All the seven foot dimensions were higher in males than females. Conclusion: There were statistically significant differences observed in all footprint dimensions between the male and female footprints except LFPI, LHBI, and RHBI.

Generation and control of multi-scroll chaotic attractors in fractional order systems

International Nuclear Information System (INIS)

Ahmad, Wajdi M.

2005-01-01

The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations

Estimation of line dimensions in 3D direct laser writing lithography

International Nuclear Information System (INIS)

Guney, M G; Fedder, G K

2016-01-01

Two photon polymerization (TPP) based 3D direct laser writing (3D-DLW) finds application in a wide range of research areas ranging from photonic and mechanical metamaterials to micro-devices. Most common structures are either single lines or formed by a set of interconnected lines as in the case of crystals. In order to increase the fidelity of these structures and reach the ultimate resolution, the laser power and scan speed used in the writing process should be chosen carefully. However, the optimization of these writing parameters is an iterative and time consuming process in the absence of a model for the estimation of line dimensions. To this end, we report a semi-empirical analytic model through simulations and fitting, and demonstrate that it can be used for estimating the line dimensions mostly within one standard deviation of the average values over a wide range of laser power and scan speed combinations. The model delimits the trend in onset of micro-explosions in the photoresist due to over-exposure and of low degree of conversion due to under-exposure. The model guides setting of high-fidelity and robust writing parameters of a photonic crystal structure without iteration and in close agreement with the estimated line dimensions. The proposed methodology is generalizable by adapting the model coefficients to any 3D-DLW setup and corresponding photoresist as a means to estimate the line dimensions for tuning the writing parameters. (paper)

Implementation of a novel two-attractor grid multi-scroll chaotic system

International Nuclear Information System (INIS)

Xiao-Hua, Luo; Zheng-Wei, Tu; Xi-Rui, Liu; Chang, Cai; Pu, Gong; Yi-Long, Liang

2010-01-01

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method. (general)

Sourcing dark matter and dark energy from α-attractors

Energy Technology Data Exchange (ETDEWEB)

Mishra, Swagat S.; Sahni, Varun [Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India); Shtanov, Yuri, E-mail: swagat@iucaa.in, E-mail: varun@iucaa.in, E-mail: shtanov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine)

2017-06-01

In [1], Kallosh and Linde drew attention to a new family of superconformal inflationary potentials, subsequently called α-attractors [2]. The α-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the α-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the α-attractors, which we call α-dark matter (αDM), shares many of the attractive features of fuzzy dark matter, with V (φ) = ½ m {sup 2}φ{sup 2}, while having none of its drawbacks. Like fuzzy dark matter, αDM can have a large Jeans length which could resolve the cusp-core and substructure problems faced by standard cold dark matter. αDM also has an appealing tracker property which enables it to converge to the late-time dark matter asymptote, ( w ) ≅ 0, from a wide range of initial conditions. It thus avoids the enormous fine-tuning problems faced by the m {sup 2}φ{sup 2} potential in describing dark matter.

Sourcing dark matter and dark energy from α-attractors

International Nuclear Information System (INIS)

Mishra, Swagat S.; Sahni, Varun; Shtanov, Yuri

2017-01-01

In [1], Kallosh and Linde drew attention to a new family of superconformal inflationary potentials, subsequently called α-attractors [2]. The α-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the α-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the α-attractors, which we call α-dark matter (αDM), shares many of the attractive features of fuzzy dark matter, with V (φ) = ½ m 2 φ 2 , while having none of its drawbacks. Like fuzzy dark matter, αDM can have a large Jeans length which could resolve the cusp-core and substructure problems faced by standard cold dark matter. αDM also has an appealing tracker property which enables it to converge to the late-time dark matter asymptote, ( w ) ≅ 0, from a wide range of initial conditions. It thus avoids the enormous fine-tuning problems faced by the m 2 φ 2 potential in describing dark matter.

Analysis of chaos attractors of MCG-recordings.

Science.gov (United States)

Jiang, Shiqin; Yang, Fan; Yi, Panke; Chen, Bo; Luo, Ming; Wang, Lemin

2006-01-01

By studying the chaos attractor of cardiac magnetic induction strength B(z) generated by the electrical activity of the heart, we found that its projection in the reconstructed phase space has a similar shape with the map of the total current dipole vector. It is worth noting that the map of the total current dipole vector is computed with MCG recordings measured at 36 locations, whereas the chaos attractor of B(z) is generated by only one cardiac magnetic field recordings on the measured plan. We discuss only two subjects of different ages in this paper.

General method to find the attractors of discrete dynamic models of biological systems

Science.gov (United States)

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

General method to find the attractors of discrete dynamic models of biological systems.

Science.gov (United States)

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

Cortical computations via transient attractors.

Directory of Open Access Journals (Sweden)

Oliver L C Rourke

Full Text Available The ability of sensory networks to transiently store information on the scale of seconds can confer many advantages in processing time-varying stimuli. How a network could store information on such intermediate time scales, between typical neurophysiological time scales and those of long-term memory, is typically attributed to persistent neural activity. An alternative mechanism which might allow for such information storage is through temporary modifications to the neural connectivity which decay on the same second-long time scale as the underlying memories. Earlier work that has explored this method has done so by emphasizing one attractor from a limited, pre-defined set. Here, we describe an alternative, a Transient Attractor network, which can learn any pattern presented to it, store several simultaneously, and robustly recall them on demand using targeted probes in a manner reminiscent of Hopfield networks. We hypothesize that such functionality could be usefully embedded within sensory cortex, and allow for a flexibly-gated short-term memory, as well as conferring the ability of the network to perform automatic de-noising, and separation of input signals into distinct perceptual objects. We demonstrate that the stored information can be refreshed to extend storage time, is not sensitive to noise in the system, and can be turned on or off by simple neuromodulation. The diverse capabilities of transient attractors, as well as their resemblance to many features observed in sensory cortex, suggest the possibility that their actions might underlie neural processing in many sensory areas.

The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data

Directory of Open Access Journals (Sweden)

Gerardo Di Martino

2017-12-01

Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.

Lorenz-like attractors in a nonholonomic model of a rattleback

International Nuclear Information System (INIS)

Gonchenko, A S; Gonchenko, S V

2015-01-01

We study chaotic dynamics in a nonholonomic model of a rattleback stone. We show that, for certain values of parameters that characterise geometrical and physical properties of the stone, a strange Lorenz-like attractor is observed in the model. We also study bifurcation scenarios for the appearance and break-down of this attractor. (paper)

Simplified Chua's attractor via bridging a diode pair

Directory of Open Access Journals (Sweden)

Quan Xu

2015-04-01

Full Text Available In this paper, a simplified Chua's circuit is realised by bridging a diode pair between a passive LC (inductance and capacitance in parallel connection - LC oscillator and an active RC (resistance and capacitance in parallel connection - RC filter. The dynamical behaviours of the circuit are investigated by numerical simulations and verified by experimental measurements. It is found that the simplified Chua's circuit generates Chua's attractors similarly and demonstrates complex non-linear phenomena including coexisting bifurcation modes and coexisting attractors in particular.

Attractors of multivalued semiflows generated by differential inclusions and their approximations

Directory of Open Access Journals (Sweden)

Alexei V. Kapustian

2000-01-01

Full Text Available We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.

Head mounted device for point-of-gaze estimation in three dimensions

DEFF Research Database (Denmark)

Hansen, Dan Witzner; Lidegaard, Morten; Krüger, Norbert

2014-01-01

This paper presents a fully calibrated extended geometric approach for gaze estimation in three dimensions (3D). The methodology is based on a geometric approach utilising a fully calibrated binocular setup constructed as a head-mounted system. The approach is based on utilisation of two ordinary...... in the horizontal and vertical dimensions regarding fixations. However, even though the workspace is limited, the fact that the system is designed as a head-mounted device, the workspace volume is relatively positioned to the pose of the device. Hence gaze can be estimated in 3D with relatively free head...

Heteroclinic cycles between unstable attractors

NARCIS (Netherlands)

Broer, Henk; Efstathiou, Konstantinos; Subramanian, Easwar

We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo-Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of

A snapshot attractor view of the advection of inertial particles in the presence of history force

Science.gov (United States)

Guseva, Ksenia; Daitche, Anton; Tél, Tamás

2017-06-01

We analyse the effect of the Basset history force on the sedimentation or rising of inertial particles in a two-dimensional convection flow. We find that the concept of snapshot attractors is useful to understand the extraordinary slow convergence due to long-term memory: an ensemble of particles converges exponentially fast towards a snapshot attractor, and this attractor undergoes a slow drift for long times. We demonstrate for the case of a periodic attractor that the drift of the snapshot attractor can be well characterized both in the space of the fluid and in the velocity space. For the case of quasiperiodic and chaotic dynamics we propose the use of the average settling velocity of the ensemble as a distinctive measure to characterize the snapshot attractor and the time scale separation corresponding to the convergence towards the snapshot attractor and its own slow dynamics.

Heteroclinic cycles between unstable attractors

International Nuclear Information System (INIS)

Broer, Henk; Efstathiou, Konstantinos; Subramanian, Easwar

2008-01-01

We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo–Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of parameter values

Hyperbolic geometry of cosmological attractors

NARCIS (Netherlands)

Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik

2015-01-01

Cosmological alpha attractors give a natural explanation for the spectral index n(s) of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial

Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics

Energy Technology Data Exchange (ETDEWEB)

Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)

2011-02-28

Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)

Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems

International Nuclear Information System (INIS)

Grassi, Giuseppe

2008-01-01

This paper presents the problem of generating four-wing (eight-wing) chaotic attractors. The adopted method consists in suitably coupling two (three) identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings (eight wings) of these novel attractors are located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues. (general)

Statistics and dimension of chaos in differential delay systems

Energy Technology Data Exchange (ETDEWEB)

Dorizzi, B.; Grammaticos, B.; Le Berre, M.; Pomeau, Y.; Ressayre, E.; Tallet, A.

1987-01-01

The chaotic solution of dissipative scalar-delay-differential equations with a nonlinear feedback periodic with respect to its argument is shown to behave as a Gaussian-Markovian process in a large time scale. The short time scale is shown to be defined by the correlation time of the delayed feedback. The dimension of the chaotic attractor is shown to be approximately equal to the number of short times that are contained inside the delay.

Statistics and dimension of chaos in differential delay systems

International Nuclear Information System (INIS)

Dorizzi, B.; Grammaticos, B.; Le Berre, M.; Pomeau, Y.; Ressayre, E.; Tallet, A.

1987-01-01

The chaotic solution of dissipative scalar-delay-differential equations with a nonlinear feedback periodic with respect to its argument is shown to behave as a Gaussian-Markovian process in a large time scale. The short time scale is shown to be defined by the correlation time of the delayed feedback. The dimension of the chaotic attractor is shown to be approximately equal to the number of short times that are contained inside the delay

Attractor controllability of Boolean networks by flipping a subset of their nodes

Science.gov (United States)

Rafimanzelat, Mohammad Reza; Bahrami, Fariba

2018-04-01

The controllability analysis of Boolean networks (BNs), as models of biomolecular regulatory networks, has drawn the attention of researchers in recent years. In this paper, we aim at governing the steady-state behavior of BNs using an intervention method which can easily be applied to most real system, which can be modeled as BNs, particularly to biomolecular regulatory networks. To this end, we introduce the concept of attractor controllability of a BN by flipping a subset of its nodes, as the possibility of making a BN converge from any of its attractors to any other one, by one-time flipping members of a subset of BN nodes. Our approach is based on the algebraic state-space representation of BNs using semi-tensor product of matrices. After introducing some new matrix tools, we use them to derive necessary and sufficient conditions for the attractor controllability of BNs. A forward search algorithm is then suggested to identify the minimal perturbation set for attractor controllability of a BN. Next, a lower bound is derived for the cardinality of this set. Two new indices are also proposed for quantifying the attractor controllability of a BN and the influence of each network variable on the attractor controllability of the network and the relationship between them is revealed. Finally, we confirm the efficiency of the proposed approach by applying it to the BN models of some real biomolecular networks.

D0-branes in black hole attractors

International Nuclear Information System (INIS)

Gaiotto, Davide; Simons, Aaron; Strominger, Andrew; Yin Xi

2006-01-01

Configurations of N probe D0-branes in a Calabi-Yau black hole are studied. A large degeneracy of near-horizon bound states are found which can be described as lowest Landau levels tiling the horizon of the black hole. These states preserve some of the enhanced supersymmetry of the near-horizon AdS 2 x S 2 x CY 3 attractor geometry, but not of the full asymptotically flat solution. Supersymmetric non-abelian configurations are constructed which, via the Myers effect, develop charges associated with higher-dimensional branes wrapping CY 3 cycles. An SU(1,1/2) superconformal quantum mechanics describing D0-branes in the attractor geometry is explicitly constructed

Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes

International Nuclear Information System (INIS)

Kachru, Shamit; Kundu, Nilay; Saha, Arpan; Samanta, Rickmoy; Trivedi, Sandip P.

2014-01-01

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS 2 ×S 3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS 2 ×S 3 geometries can in turn be connected to AdS 5 spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS 5 spacetime. The asymptotic AdS 5 spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points

Accurate path integration in continuous attractor network models of grid cells.

Science.gov (United States)

Burak, Yoram; Fiete, Ila R

2009-02-01

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Using periodic modulation to control coexisting attractors induced by delayed feedback

International Nuclear Information System (INIS)

Martinez-Zerega, B.E.; Pisarchik, A.N.; Tsimring, L.S.

2003-01-01

A delay in feedback can stabilize simultaneously several unstable periodic orbits embedded in a chaotic attractor. We show that by modulating the feedback variable it is possible to lock one of these states and eliminate other coexisting periodic attractors. The method is demonstrated with both a logistic map and a CO 2 laser model

On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator

International Nuclear Information System (INIS)

Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.

1999-01-01

The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)

The Gain Estimation of a Fabry-Perot Cavity (FPC Antenna with a Finite Dimension

Directory of Open Access Journals (Sweden)

Taek-Sun Kwon

2017-10-01

Full Text Available In this paper, we have presented an equation for estimating the gain of a Fabry-Perot cavity (FPC antenna with a finite dimension. When an FPC antenna has an infinite dimension and its height is half of a wavelength, the maximum gain of that FPC antenna can be obtained theoretically. If the FPC antenna does not have a dimension sufficient for multiple reflections between a partially reflective surface (PRS and the ground, its gain must be less than that of an FPC antenna that has an infinite dimension. In addition, the gain of an FPC antenna increases as the dimension of a PRS increases and becomes saturated from a specific dimension. The specific dimension where the gain starts to saturate also gets larger as the reflection magnitude of the PRS becomes closer to one. Thus, it would be convenient to have a gain equation when considering the dimension of an FPC antenna in order to estimate the exact gain of the FPC antenna with a specific dimension. A gain versus the dimension of the FPC antenna for various reflection magnitudes of PRS has been simulated, and the modified gain equation is produced through the curve fitting of the full-wave simulation results. The resulting empirical gain equation of an FPC antenna whose PRS dimension is larger than 1.5λ0 has been obtained.

Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap

International Nuclear Information System (INIS)

Qu Shixian; Lu Yongzhi; Zhang Lin; He Daren

2008-01-01

Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-11, period-6, chaotic band-12 and band-6 attractors. They are induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically. (general)

Co-existing hidden attractors in a radio-physical oscillator system

DEFF Research Database (Denmark)

Kuznetsov, A. P.; Kuznetsov, S. P.; Mosekilde, Erik

2015-01-01

The term `hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point...... frequency, describe the bifurcations through which hidden attractors of different type arise and disappear, and illustrate the form of the basins of attraction....

Coexisting multiple attractors and riddled basins of a memristive system.

Science.gov (United States)

Wang, Guangyi; Yuan, Fang; Chen, Guanrong; Zhang, Yu

2018-01-01

In this paper, a new memristor-based chaotic system is designed, analyzed, and implemented. Multistability, multiple attractors, and complex riddled basins are observed from the system, which are investigated along with other dynamical behaviors such as equilibrium points and their stabilities, symmetrical bifurcation diagrams, and sustained chaotic states. With different sets of system parameters, the system can also generate various multi-scroll attractors. Finally, the system is realized by experimental circuits.

Controllable V-Shape Multi-Scroll Butterfly Attractor: System and Circuit Implementation

KAUST Repository

Zidan, Mohammed A.; Radwan, Ahmed G.; Salama, Khaled N.

2012-01-01

In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable). © 2012 World Scientific Publishing Company.

Controllable V-Shape Multi-Scroll Butterfly Attractor: System and Circuit Implementation

KAUST Repository

Zidan, Mohammed A.

2012-07-23

In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable). © 2012 World Scientific Publishing Company.

Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

Science.gov (United States)

Wang, Xiaohu; Lu, Kening; Wang, Bixiang

2018-01-01

In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.

Non-Abelian magnetized blackholes and unstable attractors

International Nuclear Information System (INIS)

Mosaffa, A.E.; Randjbar-Daemi, S.; Sheikh-Jabbari, M.M.

2006-12-01

Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstroem blackholes or the AdS 2 x S 2 , are also unstable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes. (author)

Torus-doubling process via strange nonchaotic attractors

International Nuclear Information System (INIS)

Mitsui, Takahito; Uenohara, Seiji; Morie, Takashi; Horio, Yoshihiko; Aihara, Kazuyuki

2012-01-01

Torus-doubling bifurcations typically occur only a finite number of times. It has been assumed that torus-doubling bifurcations in quasiperiodically forced systems are interrupted by the appearance of strange nonchaotic attractors (SNAs). In the present Letter, we study a quasiperiodically forced noninvertible map and report the occurrence of a torus-doubling process via SNAs. The mechanism of this process is numerically clarified. Furthermore, this process is experimentally demonstrated in a switched-capacitor integrated circuit. -- Highlights: ► We report the occurrence of a torus-doubling process via strange nonchaotic attractors (SNAs). ► The process consists of the gradual fractalization of a torus and the Heagy–Hammel transition. ► The torus-doubling process via SNAs is also experimentally demonstrated in an electronic circuit.

A New Chaotic Attractor with Quadratic Exponential Nonlinear Term from Chen’s Attractor

Directory of Open Access Journals (Sweden)

Iftikhar Ahmed

2014-02-01

Full Text Available In this paper a new three-dimensional chaotic system is proposed, which relies on a nonlinear exponential term and a nonlinear quadratic cross term necessary for folding trajectories. Basic dynamical characteristics of the new system are analyzed. Compared with the Chen system, the equilibrium points of the new system does not contain the origin, and has a greater positive Lyapunov index, can produce more complex shaped chaotic attractor.

On the renormalization group perspective of α-attractors

Energy Technology Data Exchange (ETDEWEB)

Narain, Gaurav, E-mail: gaunarain@itp.ac.cn [Kavli Institute for Theoretical Physics China (KITPC), Key Laboratory of Theoretical Physics, Institute of Theoretical Physics (ITP), Chinese Academy of Sciences -CAS, Beijing 100190 (China)

2017-10-01

In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.

Generating multi-double-scroll attractors via nonautonomous approach.

Science.gov (United States)

Hong, Qinghui; Xie, Qingguo; Shen, Yi; Wang, Xiaoping

2016-08-01

It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.

How additive noise generates a phantom attractor in a model with cubic nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Bashkirtseva, Irina; Ryashko, Lev, E-mail: lev.ryashko@urfu.ru

2016-10-07

Two-dimensional nonlinear system forced by the additive noise is studied. We show that an increasing noise shifts random states and localizes them in a zone far from deterministic attractors. This phenomenon of the generation of the new “phantom” attractor is investigated on the base of probability density functions, mean values and variances of random states. We show that increasing noise results in the qualitative changes of the form of pdf, sharp shifts of mean values, and spikes of the variance. To clarify this phenomenon mathematically, we use the fast–slow decomposition and averaging over the fast variable. For the dynamics of the mean value of the slow variable, a deterministic equation is derived. It is shown that equilibria and the saddle-node bifurcation point of this deterministic equation well describe the stochastic phenomenon of “phantom” attractor in the initial two-dimensional stochastic system. - Highlights: • Two-dimensional nonlinear system with cubic nonlinearity is studied. • Additive noise generates a new phantom attractor. • By averaging over the fast variable one-dimensional equation is derived. • Phantom attractor appearance is analyzed by bifurcation analysis of this equation.

Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach

Science.gov (United States)

Tantet, A.; Lucarini, V.; Lunkeit, F.; Dijkstra, H. A.

2015-12-01

The rough response to a smooth parameter change of some non-chaotic climate models, such as the warm to snowball-Earth transition in energy balance models due to the ice-albedo feedback, can be studied in the framework of bifurcation theory, in particular by analysing the Lyapunov spectrum of fixed points or periodic orbits. However, bifurcation theory is of little help to study the destruction of a chaotic attractor which can occur in high-dimensional General Circulation Models (GCM). Yet, one would expect critical slowing down to occur before the crisis, since, as the system becomes susceptible to the physical instability mechanism responsible for the crisis, it turns out to be less and less resilient to exogenous perturbations and to spontaneous fluctuations due to other types of instabilities on the attractor. The statistical physics framework, extended to nonequilibrium systems, is particularly well suited for the study of global properties of chaotic and stochastic systems. In particular, the semigroup of transfer operators governs the evolution of distributions in phase space and its spectrum characterises both the relaxation rate of distributions to a statistical steady-state and the stability of this steady-state to perturbations. If critical slowing down indeed occurs in the approach to an attractor crisis, the gap in the spectrum of the semigroup of transfer operators is expected to shrink. We show that the chaotic attractor crisis due to the ice-albedo feedback and resulting in a transition from a warm to a snowball-Earth in the Planet Simulator (PlaSim), a GCM of intermediate complexity, is associated with critical slowing down, as observed by the slower decay of correlations before the crisis (cf. left panel). In addition, we demonstrate that this critical slowing down can be traced back to the shrinkage of the gap between the leading eigenvalues of coarse-grained approximations of the transfer operators and that these eigenvalues capture the

Estimating the level of dynamical noise in time series by using fractal dimensions

Energy Technology Data Exchange (ETDEWEB)

Sase, Takumi, E-mail: sase@sat.t.u-tokyo.ac.jp [Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 153-8505 (Japan); Ramírez, Jonatán Peña [CONACYT Research Fellow, Center for Scientific Research and Higher Education at Ensenada (CICESE), Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860, Ensenada, Baja California (Mexico); Kitajo, Keiichi [BSI-Toyota Collaboration Center, RIKEN Brain Science Institute, Wako, Saitama 351-0198 (Japan); Aihara, Kazuyuki; Hirata, Yoshito [Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 153-8505 (Japan); Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505 (Japan)

2016-03-11

We present a method for estimating the dynamical noise level of a ‘short’ time series even if the dynamical system is unknown. The proposed method estimates the level of dynamical noise by calculating the fractal dimensions of the time series. Additionally, the method is applied to EEG data to demonstrate its possible effectiveness as an indicator of temporal changes in the level of dynamical noise. - Highlights: • A dynamical noise level estimator for time series is proposed. • The estimator does not need any information about the dynamics generating the time series. • The estimator is based on a novel definition of time series dimension (TSD). • It is demonstrated that there exists a monotonic relationship between the • TSD and the level of dynamical noise. • We apply the proposed method to human electroencephalographic data.

Estimating the level of dynamical noise in time series by using fractal dimensions

International Nuclear Information System (INIS)

Sase, Takumi; Ramírez, Jonatán Peña; Kitajo, Keiichi; Aihara, Kazuyuki; Hirata, Yoshito

2016-01-01

We present a method for estimating the dynamical noise level of a ‘short’ time series even if the dynamical system is unknown. The proposed method estimates the level of dynamical noise by calculating the fractal dimensions of the time series. Additionally, the method is applied to EEG data to demonstrate its possible effectiveness as an indicator of temporal changes in the level of dynamical noise. - Highlights: • A dynamical noise level estimator for time series is proposed. • The estimator does not need any information about the dynamics generating the time series. • The estimator is based on a novel definition of time series dimension (TSD). • It is demonstrated that there exists a monotonic relationship between the • TSD and the level of dynamical noise. • We apply the proposed method to human electroencephalographic data.

From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks.

Science.gov (United States)

Tian, Daxin; Zhou, Jianshan; Sheng, Zhengguo; Wang, Yunpeng; Ma, Jianming

2016-03-14

The management of varying traffic flows essentially depends on signal controls at intersections. However, design an optimal control that considers the dynamic nature of a traffic network and coordinates all intersections simultaneously in a centralized manner is computationally challenging. Inspired by the stable gene expressions of Escherichia coli in response to environmental changes, we explore the robustness and adaptability performance of signalized intersections by incorporating a biological mechanism in their control policies, specifically, the evolution of each intersection is induced by the dynamics governing an adaptive attractor selection in cells. We employ a mathematical model to capture such biological attractor selection and derive a generic, adaptive and distributed control algorithm which is capable of dynamically adapting signal operations for the entire dynamical traffic network. We show that the proposed scheme based on attractor selection can not only promote the balance of traffic loads on each link of the network but also allows the global network to accommodate dynamical traffic demands. Our work demonstrates the potential of bio-inspired intelligence emerging from cells and provides a deep understanding of adaptive attractor selection-based control formation that is useful to support the designs of adaptive optimization and control in other domains.

Spike frequency adaptation is a possible mechanism for control of attractor preference in auto-associative neural networks

Science.gov (United States)

Roach, James; Sander, Leonard; Zochowski, Michal

Auto-associative memory is the ability to retrieve a pattern from a small fraction of the pattern and is an important function of neural networks. Within this context, memories that are stored within the synaptic strengths of networks act as dynamical attractors for network firing patterns. In networks with many encoded memories, some attractors will be stronger than others. This presents the problem of how networks switch between attractors depending on the situation. We suggest that regulation of neuronal spike-frequency adaptation (SFA) provides a universal mechanism for network-wide attractor selectivity. Here we demonstrate in a Hopfield type attractor network that neurons minimal SFA will reliably activate in the pattern corresponding to a local attractor and that a moderate increase in SFA leads to the network to converge to the strongest attractor state. Furthermore, we show that on long time scales SFA allows for temporal sequences of activation to emerge. Finally, using a model of cholinergic modulation within the cortex we argue that dynamic regulation of attractor preference by SFA could be critical for the role of acetylcholine in attention or for arousal states in general. This work was supported by: NSF Graduate Research Fellowship Program under Grant No. DGE 1256260 (JPR), NSF CMMI 1029388 (MRZ) and NSF PoLS 1058034 (MRZ & LMS).

Attractor dynamics in local neuronal networks

Directory of Open Access Journals (Sweden)

Jean-Philippe eThivierge

2014-03-01

Full Text Available Patterns of synaptic connectivity in various regions of the brain are characterized by the presence of synaptic motifs, defined as unidirectional and bidirectional synaptic contacts that follow a particular configuration and link together small groups of neurons. Recent computational work proposes that a relay network (two populations communicating via a third, relay population of neurons can generate precise patterns of neural synchronization. Here, we employ two distinct models of neuronal dynamics and show that simulated neural circuits designed in this way are caught in a global attractor of activity that prevents neurons from modulating their response on the basis of incoming stimuli. To circumvent the emergence of a fixed global attractor, we propose a mechanism of selective gain inhibition that promotes flexible responses to external stimuli. We suggest that local neuronal circuits may employ this mechanism to generate precise patterns of neural synchronization whose transient nature delimits the occurrence of a brief stimulus.

Feigenbaum attractor and intermittency in particle collisions

International Nuclear Information System (INIS)

Batunin, A.V.

1992-01-01

The hypothesis is proposed that the Feigenbaum attractor arising as a limit set in an infinite pichfork bifurcation sequence for unimodal one-dimensional maps underlies the intermittency phenomena in particle collisions. 23 refs.; 8 figs

Topological and metric properties of Henon-type strange attractors

International Nuclear Information System (INIS)

Cvitanovic, P.; Gunaratne, G.H.; Procaccia, I.

1988-01-01

We use the set of all periodic points of Henon-type mappings to develop a theory of the topological and metric properties of their attractors. The topology of a Henon-type attractor is conveniently represented by a two-dimensional symbol plane, with the allowed and disallowed orbits cleanly separated by the ''pruning front.'' The pruning front is a function discontinuous on every binary rational number, but for maps with finite dissipation chemical bondbchemical bond<1, it is well approximated by a few steps, or, in the symbolic dynamics language, by a finite grammar. Thus equipped with the complete list of allowed periodic points, we reconstruct (to resolution of order b/sup n/) the physical attractor by piecing together the linearized neighborhoods of all periodic points of cycle length n. We use this representation to compute the singularity spectrum f(α). The description in terms of periodic points works very well in the ''hyperbolic phase,'' for α larger than some α/sub c/, where α/sub c/ is the value of α corresponding to the (conjectured) phase transition

Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system

Science.gov (United States)

Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre

2018-01-01

This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

Generating multi-double-scroll attractors via nonautonomous approach

Energy Technology Data Exchange (ETDEWEB)

Hong, Qinghui; Xie, Qingguo, E-mail: qgxie@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics, Wuhan 430074 (China); Shen, Yi; Wang, Xiaoping [School of Automation, Huazhong University of Science and Technology, Wuhan 430074 (China)

2016-08-15

It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.

A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

International Nuclear Information System (INIS)

Guo-Si, Hu

2009-01-01

There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs

Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators

International Nuclear Information System (INIS)

Giacomin, Giambattista; Pakdaman, Khashayar; Pellegrin, Xavier

2012-01-01

We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long-term dynamics of this model is finite dimensional. Following this, we prove that the global attractor of this model takes one of two forms. When coupling strength is below a critical value, the global attractor is a single equilibrium point corresponding to an incoherent state. Otherwise, when coupling strength is beyond this critical value, the global attractor is a two-dimensional disc composed of radial trajectories connecting a saddle-point equilibrium (the incoherent state) to an invariant closed curve of locally stable equilibria (partially synchronized state). Our analysis hinges, on the one hand, upon sharp existence and uniqueness results and their consequence for the existence of a global attractor, and, on the other hand, on the study of the dynamics in the vicinity of the incoherent and coherent (or synchronized) equilibria. We prove in particular nonlinear stability of each synchronized equilibrium, and normal hyperbolicity of the set of such equilibria. We explore mathematically and numerically several properties of the global attractor, in particular we discuss the limit of this attractor as noise intensity decreases to zero

Detecting small attractors of large Boolean networks by function-reduction-based strategy.

Science.gov (United States)

Zheng, Qiben; Shen, Liangzhong; Shang, Xuequn; Liu, Wenbin

2016-04-01

Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behaviour of systems. A central aim of Boolean-network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP-hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.

Separation of attractors in 1-modulus quantum corrected special geometry

CERN Document Server

Bellucci, S; Marrani, A; Shcherbakov, A

2008-01-01

We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...

Learning rate and attractor size of the single-layer perceptron

International Nuclear Information System (INIS)

Singleton, Martin S.; Huebler, Alfred W.

2007-01-01

We study the simplest possible order one single-layer perceptron with two inputs, using the delta rule with online learning, in order to derive closed form expressions for the mean convergence rates. We investigate the rate of convergence in weight space of the weight vectors corresponding to each of the 14 out of 16 linearly separable rules. These vectors follow zigzagging lines through the piecewise constant vector field to their respective attractors. Based on our studies, we conclude that a single-layer perceptron with N inputs will converge in an average number of steps given by an Nth order polynomial in (t/l), where t is the threshold, and l is the size of the initial weight distribution. Exact values for these averages are provided for the five linearly separable classes with N=2. We also demonstrate that the learning rate is determined by the attractor size, and that the attractors of a single-layer perceptron with N inputs partition R N +R N

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Science.gov (United States)

Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben

2018-04-01

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

Hidden Attractors in a Model of a Bubble Contrast Agent Oscillating Near an Elastic Wall

Science.gov (United States)

Garashchuk, Ivan; Sinelshchikov, Dmitry; Kudryashov, Nikolay

2018-02-01

A model describing the dynamics of a spherical gas bubble in a compressible viscous liquid is studied. The bubble is oscillating close to an elastic wall of finite thickness under the influence of an external pressure field which simulates a contrast agent oscillating close to a blood vessel wall. Here we investigate numerically the coexistence of chaotic and periodic attractors in this model. One of the tools applied for seeking coexisting attractors is the perpetual points method. This method can be helpful for localizing coexisting attractors, occurring in various physically realistic ranges of variation of the control parameters. We provide some examples of coexisting attractors to demonstrate the importance of the multistability problem for the applications.

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

Science.gov (United States)

Vautard, R.; Ghil, M.

1989-01-01

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

An efficient algorithm for computing fixed length attractors based on bounded model checking in synchronous Boolean networks with biochemical applications.

Science.gov (United States)

Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N

2015-04-28

Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.

Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)

2016-09-15

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.

Attractors of dissipative structure in three dissipative fluids

International Nuclear Information System (INIS)

Kondoh, Yoshiomi

1993-10-01

A general theory with use of auto-correlations for distributions is presented to derive that realization of coherent structures in general dissipative dynamic systems is equivalent to that of self-organized states with the minimum dissipation rate for instantaneously contained energy. Attractors of dissipative structure are shown to be given by eigenfunctions for dissipative dynamic operators of the dynamic system and to constitute the self-organized and self-similar decay phase. Three typical examples applied to incompressible viscous fluids, to incompressible viscous and resistive magnetohydrodynamic (MHD) fluids and to compressible resistive MHD plasmas are presented to lead to attractors in the three dissipative fluids and to describe a common physical picture of self-organization and bifurcation of the dissipative structure. (author)

Approximate convex hull of affine iterated function system attractors

International Nuclear Information System (INIS)

Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

2012-01-01

Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

Multistability and hidden attractors in a multilevel DC/DC converter

DEFF Research Database (Denmark)

Zhusubaliyev, Zhanybai T.; Mosekilde, Erik

2015-01-01

An attracting periodic, quasiperiodic or chaotic set of a smooth, autonomous system may be referred to as a "hidden attractor" if its basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Historically, this condition has implied that the basin of attraction...... produce complicated structures of attracting and repelling states organized around the basic switching cycle. This leads us to suggest the existence of hidden attractors in such systems as well. In this case, the condition will be that the basin of attraction does not overlap with the fixed point...

Statistical properties of chaotic dynamical systems which exhibit strange attractors

International Nuclear Information System (INIS)

Jensen, R.V.; Oberman, C.R.

1981-07-01

A path integral method is developed for the calculation of the statistical properties of turbulent dynamical systems. The method is applicable to conservative systems which exhibit a transition to stochasticity as well as dissipative systems which exhibit strange attractors. A specific dissipative mapping is considered in detail which models the dynamics of a Brownian particle in a wave field with a broad frequency spectrum. Results are presented for the low order statistical moments for three turbulent regimes which exhibit strange attractors corresponding to strong, intermediate, and weak collisional damping

Universality of multi-field α-attractors

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Achúcarro, Ana; Kallosh, Renata; Linde, Andrei; Wang, Dong-Gang; Welling, Yvette

2018-04-01

We study a particular version of the theory of cosmological α-attractors with α=1/3, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal Script N=4 superconformal symmetry and from maximal Script N=8 supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to significant modifications of the axion potential: nssimeq1‑2/N, rsimeq4/N2. We also show that the universality of predictions extends to other values of α lesssim Script O(1) with general two-field potentials that may or may not have an embedding in supergravity. Our results support the idea that inflation involving multiple, not stabilized, light fields on a hyperbolic manifold may be compatible with current observational constraints for a broad class of potentials.

Visual tool for estimating the fractal dimension of images

Science.gov (United States)

Grossu, I. V.; Besliu, C.; Rusu, M. V.; Jipa, Al.; Bordeianu, C. C.; Felea, D.

2009-10-01

This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from "noise", we considered also the family of all band-pass filters with the same band-width (specified as parameter). The fractal dimension can be thus represented as a function of the pixel color code. The program was used for the study of paintings cracks, as an additional tool which can help the critic to decide if an artistic work is original or not. Program summaryProgram title: Fractal Analysis v01 Catalogue identifier: AEEG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29 690 No. of bytes in distributed program, including test data, etc.: 4 967 319 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30M Classification: 14 Nature of problem: Estimating the fractal dimension of images. Solution method: Optimized implementation of the box-counting algorithm. Use of a band-pass filter for separating the real information from "noise". User friendly graphical interface. Restrictions: Although various file-types can be used, the application was mainly conceived for the 8-bit grayscale, windows bitmap file format. Running time: In a first approximation, the algorithm is linear.

Multiple attractors and crisis route to chaos in a model food-chain

International Nuclear Information System (INIS)

Upadhyay, Ranjit Kumar

2003-01-01

An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out. The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors. Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics. The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain. We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a 1 =1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation. Multiple attractors with riddled basins and fractal boundaries are also observed. If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation. Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable

Is Cygus X-1 a chaotic dynamical system?

International Nuclear Information System (INIS)

Unno, Wasaburo; Yoneyama, Tadaoki; Urata, Kenji; Masaki, Isao; Kondo, Masa-aki; Inoue, Hajime.

1990-01-01

X-ray data of Cyg X-1 observed by the Tenma satellite were analyzed to determine whether Cyg X-1 is a chaotic dynamical system of low dimension. Since Poisson noise disturbs the determination of the attractor dimension of the system, comparative studies were carried out for the Cyg X-1 data relative to artificial data of purely stochastic Poisson noise and to a Lorenz attractor plus noise. The attractor dimension was searched using trajectories of time series data in phase space, the dimension of which was varied up to 21. The relation between the attractor dimension and the phase-space dimension for the Cyg X-1 data starts to deviate from that of noise data from a phase-space dimension of about 7, showing the presence of an attractor with a dimension of about 7 or less. Though three positive Lyapunov exponents were calculated, they are too small (∼10 -2 ) to prove with certainty that the Cyg X-1 attractor should be a strange attractor. (author)

An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks

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Cabessa, Jérémie; Villa, Alessandro E. P.

2014-01-01

We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits. PMID:24727866

Investigating parameters participating in the infant respiratory control system attractor.

Science.gov (United States)

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2008-01-01

Theoretically, any participating parameter in a non-linear system represents the dynamics of the whole system. Taken's time delay embedding theory provides the fundamental basis for allowing non-linear analysis to be performed on physiological, time-series data. In practice, only one measurable parameter is required to be measured to convey an accurate representation of the system dynamics. In this paper, the infant respiratory control system is represented using three variables-a digitally sampled respiratory inductive plethysmography waveform, and the derived parameters tidal volume and inter-breath interval time series data. For 14 healthy infants, these data streams were analysed using recurrence plot analysis across one night of sleep. The measured attractor size of these variables followed the same qualitative trends across the nights study. Results suggest that the attractor size measures of the derived IBI and tidal volume are representative surrogates for the raw respiratory waveform. The extent to which the relative attractor sizes of IBI and tidal volume remain constant through changing sleep state could potentially be used to quantify pathology, or maturation of breathing control.

A signature of attractor dynamics in the CA3 region of the hippocampus.

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César Rennó-Costa

2014-05-01

Full Text Available The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These "attract" the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion. The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be "attracted" to a stored pattern. However, contrary to previous expectations, as a pattern is gradually "morphed" from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.

Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors

Science.gov (United States)

Wei, Zhouchao; Rajagopal, Karthikeyan; Zhang, Wei; Kingni, Sifeu Takougang; Akgül, Akif

2018-04-01

Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke-Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.

Shift of critical points in the parametrically modulated Henon map with coexisting attractors

International Nuclear Information System (INIS)

Saucedo-Solorio, J.M.; Pisarchik, A.N.; Aboites, V.

2002-01-01

We study how the critical point positions change in the parametrically modulated Henon map with coexisting period-1 and period-3 attractors. In particular, a new type of scaling law is found coinciding with that evidenced by laser experiments. We show that resonance phenomena play a crucial role in deformation of attractors and their basins of attraction

Estimation of stature from hand and foot dimensions in a Korean population.

Science.gov (United States)

Kim, Wonjoon; Kim, Yong Min; Yun, Myung Hwan

2018-04-01

The estimation of stature using foot and hand dimensions is essential in the process of personal identification. The shapes of feet and hands vary depending on races and gender, and it is of great importance to design an adequate equation in consideration of variances to estimate stature. This study is based on a total of 5,195 South Korean males and females, aged from 20 to 59 years. Body dimensions of stature, hand length, hand breadth, foot length, and foot breadth were measured according to standard anthropometric procedures. The independent t-test was performed in order to verify significant gender-induced differences and the results showed that there was significant difference between males and females for all the foot-hand dimensions (pfoot length showed highest correlation, whereas the hand breadth showed least correlation. The stepwise regression analysis was conducted, and the results showed that males had the highest prediction accuracy in the regression equation consisting of foot length and hand length (R 2 =0.532), whereas females had the highest accuracy in the regression model consisting of foot length and hand breadth (R 2 =0.437) The findings of this study indicated that hand and foot dimensions can be used to predict the stature of South Korean in the forensic science field. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Non-Abelian magnetized blackholes and unstable attractors

Energy Technology Data Exchange (ETDEWEB)

Mosaffa, A.E. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: mosaffa@theory.ipm.ac.ir; Randjbar-Daemi, S. [The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11 34014, Trieste (Italy)], E-mail: seif@ictp.trieste.it; Sheikh-Jabbari, M.M. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: jabbari@theory.ipm.ac.ir

2008-01-21

Fluctuations of non-Abelian gauge fields in a background magnetic charge contain 'tachyonic' modes which as we will show cause an instability of the background. We extend this result to the cases where the background charge (flux) is coupled to four-dimensional Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of (colored) Reissner-Nordstroem blackholes or the AdS{sub 2}xS{sup 2}, are also unstable unless the flux assumes its smallest allowed value, in which case the configuration is stable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes, with the exception of the minimally charged stable ones.

Google matrix, dynamical attractors, and Ulam networks.

Science.gov (United States)

Shepelyansky, D L; Zhirov, O V

2010-03-01

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as two characteristics similar to the web: a power-law decay in PageRank that mirrors the decay of PageRank on the world wide web and a sensitivity to the value alpha in PageRank. The simple dynamical attractors play here the role of popular websites with a strong concentration of PageRank. A variation in the Google parameter alpha or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.

Recurrence quantification analysis in Liu's attractor

International Nuclear Information System (INIS)

Balibrea, Francisco; Caballero, M. Victoria; Molera, Lourdes

2008-01-01

Recurrence Quantification Analysis is used to detect transitions chaos to periodical states or chaos to chaos in a new dynamical system proposed by Liu et al. This system contains a control parameter in the second equation and was originally introduced to investigate the forming mechanism of the compound structure of the chaotic attractor which exists when the control parameter is zero

Excavation of attractor modules for nasopharyngeal carcinoma via integrating systemic module inference with attract method.

Science.gov (United States)

Jiang, T; Jiang, C-Y; Shu, J-H; Xu, Y-J

2017-07-10

The molecular mechanism of nasopharyngeal carcinoma (NPC) is poorly understood and effective therapeutic approaches are needed. This research aimed to excavate the attractor modules involved in the progression of NPC and provide further understanding of the underlying mechanism of NPC. Based on the gene expression data of NPC, two specific protein-protein interaction networks for NPC and control conditions were re-weighted using Pearson correlation coefficient. Then, a systematic tracking of candidate modules was conducted on the re-weighted networks via cliques algorithm, and a total of 19 and 38 modules were separately identified from NPC and control networks, respectively. Among them, 8 pairs of modules with similar gene composition were selected, and 2 attractor modules were identified via the attract method. Functional analysis indicated that these two attractor modules participate in one common bioprocess of cell division. Based on the strategy of integrating systemic module inference with the attract method, we successfully identified 2 attractor modules. These attractor modules might play important roles in the molecular pathogenesis of NPC via affecting the bioprocess of cell division in a conjunct way. Further research is needed to explore the correlations between cell division and NPC.

Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System

Directory of Open Access Journals (Sweden)

Wenyu Yang

2014-01-01

Full Text Available Particle swarm optimization (PSO is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE. In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems.

The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System

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Yongjun Li

2016-01-01

Full Text Available First, for a process U(t,τ∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t∣t≤T, for any T∈R, satisfying the following: (i M(t is compact, (ii M(t is positively invariant, that is, U(t,τM(τ⊂M(t, and (iii there exist k,l>0 such that dist(U(t,τB(τ,M(t≤ke-(t-τ; that is, M(t pullback exponential attracts B(τ. Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force.

Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime.

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Forest, M Gregory; Wang, Qi; Zhou, Ruhai

2015-08-28

Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic

A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

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Qiang Lai

2017-12-01

Full Text Available This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

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Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

Attractor merging crisis in chaotic business cycles

International Nuclear Information System (INIS)

Chian, Abraham C.-L.; Borotto, Felix A.; Rempel, Erico L.; Rogers, Colin

2005-01-01

A numerical study is performed on a forced-oscillator model of nonlinear business cycles. An attractor merging crisis due to a global bifurcation is analyzed using the unstable periodic orbits and their associated stable and unstable manifolds. Characterization of crisis can improve our ability to forecast sudden major changes in economic systems

Comparison of surface fractal dimensions of chromizing coating and P110 steel for corrosion resistance estimation

International Nuclear Information System (INIS)

Lin, Naiming; Guo, Junwen; Xie, Faqin; Zou, Jiaojuan; Tian, Wei; Yao, Xiaofei; Zhang, Hongyan; Tang, Bin

2014-01-01

Highlights: • Continuous chromizing coating was synthesized on P110 steel by pack cementation. • The chromizing coating showed better corrosion resistance. • Comparison of surface fractal dimensions can estimate corrosion resistance. - Abstract: In the field of corrosion research, mass gain/loss, electrochemical tests and comparing the surface elemental distributions, phase constitutions as well as surface morphologies before and after corrosion are extensively applied to investigate the corrosion behavior or estimate the corrosion resistance of materials that operated in various environments. Most of the above methods are problem oriented, complex and longer-period time-consuming. However from an object oriented point of view, the corroded surfaces of materials often have self-similar characterization: fractal property which can be employed to efficiently achieve damaged surface analysis. The present work describes a strategy of comparison of the surface fractal dimensions for corrosion resistance estimation: chromizing coating was synthesized on P110 steel surface to improve its performance via pack cementation. Scanning electron microscope (SEM) was used to investigate the surface morphologies of the original and corroded samples. Surface fractal dimensions of the detected samples were calculated by binary images related to SEM images of surface morphologies with box counting algorithm method. The results showed that both surface morphologies and surface fractal dimensions of P110 steel varied greatly before and after corrosion test, but the chromizing coating changed slightly. The chromizing coating indicated better corrosion resistance than P110 steel. Comparison of surface fractal dimensions of original and corroded samples can rapidly and exactly realize the estimation of corrosion resistance

Comparison of surface fractal dimensions of chromizing coating and P110 steel for corrosion resistance estimation

Energy Technology Data Exchange (ETDEWEB)

Lin, Naiming, E-mail: lnmlz33@163.com [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Guo, Junwen [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Xie, Faqin [School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072 (China); Zou, Jiaojuan; Tian, Wei [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Yao, Xiaofei [School of Materials and Chemical Engineering, Xi’an Technological University, Xi’an 710032 (China); Zhang, Hongyan; Tang, Bin [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China)

2014-08-30

Highlights: • Continuous chromizing coating was synthesized on P110 steel by pack cementation. • The chromizing coating showed better corrosion resistance. • Comparison of surface fractal dimensions can estimate corrosion resistance. - Abstract: In the field of corrosion research, mass gain/loss, electrochemical tests and comparing the surface elemental distributions, phase constitutions as well as surface morphologies before and after corrosion are extensively applied to investigate the corrosion behavior or estimate the corrosion resistance of materials that operated in various environments. Most of the above methods are problem oriented, complex and longer-period time-consuming. However from an object oriented point of view, the corroded surfaces of materials often have self-similar characterization: fractal property which can be employed to efficiently achieve damaged surface analysis. The present work describes a strategy of comparison of the surface fractal dimensions for corrosion resistance estimation: chromizing coating was synthesized on P110 steel surface to improve its performance via pack cementation. Scanning electron microscope (SEM) was used to investigate the surface morphologies of the original and corroded samples. Surface fractal dimensions of the detected samples were calculated by binary images related to SEM images of surface morphologies with box counting algorithm method. The results showed that both surface morphologies and surface fractal dimensions of P110 steel varied greatly before and after corrosion test, but the chromizing coating changed slightly. The chromizing coating indicated better corrosion resistance than P110 steel. Comparison of surface fractal dimensions of original and corroded samples can rapidly and exactly realize the estimation of corrosion resistance.

Laboratory and numerical simulation of internal wave attractors and their instability.

Science.gov (United States)

Brouzet, Christophe; Dauxois, Thierry; Ermanyuk, Evgeny; Joubaud, Sylvain; Sibgatullin, Ilias

2015-04-01

Internal wave attractors are formed as result of focusing of internal gravity waves in a confined domain of stably stratified fluid due to peculiarities of reflections properties [1]. The energy injected into domain due to external perturbation, is concentrated along the path formed by the attractor. The existence of attractors was predicted theoretically and proved both experimentally and numerically [1-4]. Dynamics of attractors is greatly influenced by geometrical focusing, viscous dissipation and nonlinearity. The experimental setup features Schmidt number equal to 700 which impose constraints on resolution in numerical schemes. Also for investigation of stability on large time intervals (about 1000 periods of external forcing) numerical viscosity may have significant impact. For these reasons, we have chosen spectral element method for investigation of this problem, what allows to carefully follow the nonlinear dynamics. We present cross-comparison of experimental observations and numerical simulations of long-term behavior of wave attractors. Fourier analysis and subsequent application of Hilbert transform are used for filtering of spatial components of internal-wave field [5]. The observed dynamics shows a complicated coupling between the effects of local instability and global confinement of the fluid domain. The unstable attractor is shown to act as highly efficient mixing box providing the efficient energy pathway from global-scale excitation to small-scale wave motions and mixing. Acknowledgement, IS has been partially supported by Russian Ministry of Education and Science (agreement id RFMEFI60714X0090) and Russian Foundation for Basic Research, grant N 15-01-06363. EVE gratefully acknowledges his appointment as a Marie Curie incoming fellow at Laboratoire de physique ENS de Lyon. This work has been partially supported by the ONLITUR grant (ANR-2011-BS04-006-01) and achieved thanks to the resources of PSMN from ENS de Lyon 1. Maas, L. R. M. & Lam, F

A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems

International Nuclear Information System (INIS)

Aguirre-Hernández, B.; Campos-Cantón, E.; López-Renteria, J.A.; Díaz González, E.C.

2015-01-01

In this paper, we consider characteristic polynomials of n-dimensional systems that determine a segment of polynomials. One parameter is used to characterize this segment of polynomials in order to determine the maximal interval of dissipativity and unstability. Then we apply this result to the generation of a family of attractors based on a class of unstable dissipative systems (UDS) of type affine linear systems. This class of systems is comprised of switched linear systems yielding strange attractors. A family of these chaotic switched systems is determined by the maximal interval of perturbation of the matrix that governs the dynamics for still having scroll attractors

Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data

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Axel Hutt

2017-05-01

Full Text Available Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recurrence structure analysis permitting the derivation of an optimal symbolic representation of metastable states and their dynamical transitions. To derive heteroclinic sequences of metastable attractors in various experimental conditions, the work introduces a Hausdorff clustering algorithm for symbolic dynamics. The application to brain signals (event-related potentials utilizing neural field models illustrates the methodology.

Attractors, universality, and inflation

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Downes, Sean; Dutta, Bhaskar; Sinha, Kuver

2012-11-01

Studies of the initial conditions for inflation have conflicting predictions from exponential suppression to inevitability. At the level of phase space, this conflict arises from the competing intuitions of CPT invariance and thermodynamics. After reviewing this conflict, we enlarge the ensemble beyond phase space to include scalar potential data. We show how this leads to an important contribution from inflection point inflation, enhancing the likelihood of inflation to a power law, 1/Ne3. In the process, we emphasize the attractor dynamics of the gravity-scalar system and the existence of universality classes from inflection point inflation. Finally, we comment on the predictivity of inflation in light of these results.

On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0

International Nuclear Information System (INIS)

Vishik, M I; Chepyzhov, V V; Titi, E S

2007-01-01

We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A 0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor A α of the Navier-Stokes-α model converges to the trajectory attractor A 0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit A min (subset or equal A 0 ) of the trajectory attractor A α as α→0+ and prove that the set A min is connected and strictly invariant. Bibliography: 35 titles.

Finite connectivity attractor neural networks

International Nuclear Information System (INIS)

Wemmenhove, B; Coolen, A C C

2003-01-01

We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous

Global attractors and extinction dynamics of cyclically competing species.

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Rulands, Steffen; Zielinski, Alejandro; Frey, Erwin

2013-05-01

Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases.

Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data

DEFF Research Database (Denmark)

Buch-Kromann, Tine; Nielsen, Jens

2012-01-01

This paper introduces a multivariate density estimator for truncated and censored data with special emphasis on extreme values based on survival analysis. A local constant density estimator is considered. We extend this estimator by means of tail flattening transformation, dimension reducing prior...

Crisis of the chaotic attractor of a climate model: a transfer operator approach

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Tantet, Alexis; Lucarini, Valerio; Lunkeit, Frank; Dijkstra, Henk A.

2018-05-01

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are known to be characterised by a single or a pair of characteristic exponents crossing the imaginary axis. As a result, the approach of such bifurcations in the presence of noise can be inferred from the slowing down of the decay of correlations (Held and Kleinen 2004 Geophys. Res. Lett. 31 1–4). On the other hand, little is known about global bifurcations involving high-dimensional attractors with several positive Lyapunov exponents. It is known that the global stability of chaotic attractors may be characterised by the spectral properties of the Koopman (Mauroy and Mezić 2016 IEEE Trans. Autom. Control 61 3356–69) or the transfer operators governing the evolution of statistical ensembles. Accordingly, it has recently been shown (Tantet 2017 J. Stat. Phys. 1–33) that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second class of resonances, the unstable resonances, are responsible for the decay of correlations and mixing on the attractor. In the deterministic case, these cannot be expected to be affected by general boundary crises. Here, however, we give an example of a chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice

Contractive function systems, their attractors and metrization

Czech Academy of Sciences Publication Activity Database

Banakh, T.; Kubiś, Wieslaw; Novosad, N.; Nowak, M.; Strobin, F.

2015-01-01

Roč. 46, č. 2 (2015), s. 1029-1066 ISSN 1230-3429 R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : fractal * attractor * iterated function system * contracting function system Subject RIV: BA - General Mathematics Impact factor: 0.717, year: 2015 http://www.apcz.pl/czasopisma/index.php/TMNA/article/view/TMNA.2015.076

Is attentional blink a byproduct of neocortical attractors?

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David N Silverstein

2011-05-01

Full Text Available This study proposes a computational model for attentional blink or blink of the mind, a phenomenon where a human subject misses perception of a later expected visual pattern as two expected visual patterns are presented less than 500 ms apart. A neocortical patch modeled as an attractor network is stimulated with a sequence of 14 patterns 100 ms apart, two of which are expected targets. Patterns that become active attractors are considered recognized. A neocortical patch is represented as a square matrix of hypercolumns, each containing a set of minicolumns with synaptic connections within and across both minicolumns and hypercolumns. Each minicolumn consists of locally connected layer 2/3 pyramidal cells with interacting basket cells and layer 4 pyramidal cells for input stimulation. All neurons are implemented using the Hodgkin-Huxley multi-compartmental cell formalism and include calcium dynamics, and they interact via saturating and depressing AMPA / NMDA and GABAA synapses. Stored patterns are encoded with global connectivity of minicolumns across hypercolumns and active patterns compete as the result of lateral inhibition in the network. Stored patterns were stimulated over time intervals to create attractor interference measurable with synthetic spike traces. This setup corresponds with item presentations in human visual attentional blink studies. Stored target patterns were depolarized while distractor patterns where hyperpolarized to represent expectation of items in working memory. Additionally, studies on the inhibitory effect of benzodiazopines on attentional blink in human subjects were compared with neocortical simulations where the GABAA receptor conductance and decay time were increased. Simulations showed increases in the attentional blink duration, agreeing with observations in human studies.

Inflationary α -attractor cosmology: A global dynamical systems perspective

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Alho, Artur; Uggla, Claes

2017-04-01

We study flat Friedmann-Lemaître-Robertson-Walker α -attractor E- and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e -folds, is associated with a particular solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this "inflationary attractor solution." A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

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Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

INFN-Laboratori Nazionali di Frascati School on the Attractor Mechanism 2009

CERN Document Server

4th School on Attractor Mechanism : Supersymmetric Gravity and Black Holes

2013-01-01

This book is based upon lectures presented in the summer of 2009 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara,  G. Dall'Agata, J.F. Morales, J. Simón and M. Trigiante. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and the related reworking of, the various contributions. It is the fifth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism.

Attractor hopping between polarization dynamical states in a vertical-cavity surface-emitting laser subject to parallel optical injection

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Denis-le Coarer, Florian; Quirce, Ana; Valle, Angel; Pesquera, Luis; Rodríguez, Miguel A.; Panajotov, Krassimir; Sciamanna, Marc

2018-03-01

We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83 ±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noise play a role in causing switching between attractors. We also find attractor hopping between chaotic states with different polarization properties. In this case, simulation results show that spontaneous emission noise inherent to the VCSEL is enough to induce this hopping.

The Photoplethismographic Signal Processed with Nonlinear Time Series Analysis Tools

International Nuclear Information System (INIS)

Hernandez Caceres, Jose Luis; Hong, Rolando; Garcia Lanz, Abel; Garcia Dominguez, Luis; Cabannas, Karelia

2001-01-01

Finger photoplethismography (PPG) signals were submitted to nonlinear time series analysis. The applied analytical techniques were: (i) High degree polynomial fitting for baseline estimation; (ii) FFT analysis for estimating power spectra; (iii) fractal dimension estimation via the Higuchi's time-domain method, and (iv) kernel nonparametric estimation for reconstructing noise free-attractors and also for estimating signal's stochastic components

Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.

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Safonov, Leonid A.; Tomer, Elad; Strygin, Vadim V.; Ashkenazy, Yosef; Havlin, Shlomo

2002-12-01

We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.

Architecture of chaotic attractors for flows in the absence of any singular point

Energy Technology Data Exchange (ETDEWEB)

Letellier, Christophe [CORIA-UMR 6614 Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray (France); Malasoma, Jean-Marc [Université de Lyon, ENTPE, Laboratoire Génie Civil et Bâtiment, 3 Rue Maurice Audin, F-69518 Vaulx-en-Velin Cedex (France)

2016-06-15

Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 × 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in the neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.

Deformation of attractor landscape via cholinergic presynaptic modulations: a computational study using a phase neuron model.

Directory of Open Access Journals (Sweden)

Takashi Kanamaru

Full Text Available Corticopetal acetylcholine (ACh is released transiently from the nucleus basalis of Meynert (NBM into the cortical layers and is associated with top-down attention. Recent experimental data suggest that this release of ACh disinhibits layer 2/3 pyramidal neurons (PYRs via muscarinic presynaptic effects on inhibitory synapses. Together with other possible presynaptic cholinergic effects on excitatory synapses, this may result in dynamic and temporal modifications of synapses associated with top-down attention. However, the system-level consequences and cognitive relevance of such disinhibitions are poorly understood. Herein, we propose a theoretical possibility that such transient modifications of connectivity associated with ACh release, in addition to top-down glutamatergic input, may provide a neural mechanism for the temporal reactivation of attractors as neural correlates of memories. With baseline levels of ACh, the brain returns to quasi-attractor states, exhibiting transitive dynamics between several intrinsic internal states. This suggests that top-down attention may cause the attention-induced deformations between two types of attractor landscapes: the quasi-attractor landscape (Q-landscape, present under low-ACh, non-attentional conditions and the attractor landscape (A-landscape, present under high-ACh, top-down attentional conditions. We present a conceptual computational model based on experimental knowledge of the structure of PYRs and interneurons (INs in cortical layers 1 and 2/3 and discuss the possible physiological implications of our results.

A cortical attractor network with Martinotti cells driven by facilitating synapses.

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Pradeep Krishnamurthy

Full Text Available The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an attractor state and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the attractor state. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.

Logical Attractors: a Boolean Approach to the Dynamics of Psychosis

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Kupper, Z.; Hoffmann, H.

A Boolean modeling approach to attractors in the dynamics of psychosis is presented: Kinetic Logic, originating from R. Thomas, describes systems on an intermediate level between a purely verbal, qualitative description and a description using nonlinear differential equations. With this method we may model impact, feedback and temporal evolution, as well as analyze the resulting attractors. In our previous research the method has been applied to general and more specific questions in the dynamics of psychotic disorders. In this paper a model is introduced that describes different dynamical patterns of chronic psychosis in the context of vocational rehabilitation. It also shows to be useful in formulating and exploring possible treatment strategies. Finally, some of the limitations and benefits of Kinetic Logic as a modeling tool for psychology and psychiatry are discussed.

Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research.

Science.gov (United States)

Golino, Hudson F; Epskamp, Sacha

2017-01-01

The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman's eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use fit indexes as BIC and EBIC and the less used and studied approach called very simple structure (VSS). In the present paper a new approach to estimate the number of dimensions will be introduced and compared via simulation to the traditional techniques pointed above. The approach proposed in the current paper is called exploratory graph analysis (EGA), since it is based on the graphical lasso with the regularization parameter specified using EBIC. The number of dimensions is verified using the walktrap, a random walk algorithm used to identify communities in networks. In total, 32,000 data sets were simulated to fit known factor structures, with the data sets varying across different criteria: number of factors (2 and 4), number of items (5 and 10), sample size (100, 500, 1000 and 5000) and correlation between factors (orthogonal, .20, .50 and .70), resulting in 64 different conditions. For each condition, 500 data sets were simulated using lavaan. The result shows that the EGA performs comparable to parallel analysis, EBIC, eBIC and to Kaiser-Guttman rule in a number of situations, especially when the number of factors was two. However, EGA was the only technique able to correctly estimate the number of dimensions in the four-factor structure when the correlation between factors were .7, showing an accuracy of 100% for a sample size of 5,000 observations. Finally, the EGA was used to estimate the number of factors in a real dataset, in order to compare its performance with the other six techniques tested in the simulation study.

Attractor horizons in six-dimensional type IIB supergravity

Energy Technology Data Exchange (ETDEWEB)

Astefanesei, Dumitru, E-mail: dumitru.astefanesei@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Miskovic, Olivera, E-mail: olivera.miskovic@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Universidad Andres Bello, Departamento de Ciencias Fisicas, Republica 220, Santiago (Chile)

2012-08-14

We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.

Split Attractor Flow in N=2 Minimally Coupled Supergravity

CERN Document Server

Ferrara, Sergio; Orazi, Emanuele

2011-01-01

We classify the stability region, marginal stability walls (MS) and split attractor flows for two-center extremal black holes in four-dimensional N=2 supergravity minimally coupled to n vector multiplets. It is found that two-center (continuous) charge orbits, classified by four duality invariants, either support a stability region ending on a MS wall or on an anti-marginal stability (AMS) wall, but not both. Therefore, the scalar manifold never contains both walls. Moreover, the BPS mass of the black hole composite (in its stability region) never vanishes in the scalar manifold. For these reasons, the "bound state transformation walls" phenomenon does not necessarily occur in these theories. The entropy of the flow trees also satisfies an inequality which forbids "entropy enigma" decays in these models. Finally, the non-BPS case, due to the existence of a "fake" superpotential satisfying a triangle inequality, can be treated as well, and it can be shown to exhibit a split attractor flow dynamics which, at le...

Hierarchical-control-based output synchronization of coexisting attractor networks

International Nuclear Information System (INIS)

Yun-Zhong, Song; Yi-Fa, Tang

2010-01-01

This paper introduces the concept of hierarchical-control-based output synchronization of coexisting attractor networks. Within the new framework, each dynamic node is made passive at first utilizing intra-control around its own arena. Then each dynamic node is viewed as one agent, and on account of that, the solution of output synchronization of coexisting attractor networks is transformed into a multi-agent consensus problem, which is made possible by virtue of local interaction between individual neighbours; this distributed working way of coordination is coined as inter-control, which is only specified by the topological structure of the network. Provided that the network is connected and balanced, the output synchronization would come true naturally via synergy between intra and inter-control actions, where the Tightness is proved theoretically via convex composite Lyapunov functions. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme. (general)

3rd School on Attractor Mechanism

CERN Document Server

SAM 2007; The Attractor Mechanism: Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007

2010-01-01

This book is based upon lectures presented in June 2007 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, M. Gunaydin, P. Levay, and T. Mohaupt. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and related reworking of, the various contributions. In addition, this volume contains contributions originating from short presentations of rece

Scaling properties of paleomagnetic reversal sequence

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S. S. Ivanov

1996-01-01

Full Text Available The history of reversals of main geomagnetic field during last 160 My is analyzed as a sequence of events, presented as a point set on the time axis. Different techniques were applied including the method of boxcounting, dispersion counter-scaling, multifractal analysis and examination of attractor behaviour in multidimensional phase space. The existence of a crossover point at time interval 0.5-1.0 My was clearly identified, dividing the whole time range into two subranges with different scaling properties. The long-term subrange is characterized by monofractal dimension 0.88 and by an attractor, whose correlation dimension converges to 1.0, that provides evidence of a deterministic dynamical system in this subrange, similar to most existing dynamo models. In the short-term subrange the fractal dimension estimated by different methods varies from 0.47 to 0.88 and the dimensionality of the attractor is obtained to be about 3.7. These results are discussed in terms of non-linear superposition of processes in the Earth's geospheres.

Our universe as an attractor in a superstring model

International Nuclear Information System (INIS)

Maeda, Keiichi.

1986-11-01

One preferential scenario of the evolution of the universe is discussed in a superstring model. The universe can reach the present state as an attractor in the dynamical system. The kinetic terms of the ''axions'' play an important role so that our present universe is realized almost uniquely. (author)

Attractor mechanism as a distillation procedure

International Nuclear Information System (INIS)

Levay, Peter; Szalay, Szilard

2010-01-01

In a recent paper it was shown that for double extremal static spherical symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of a Greenberger-Horne-Zeilinger type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges, the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a Greenberger-Horne-Zeilinger state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.

Internal wave attractors: different scenarios of instability

OpenAIRE

Brouzet, Christophe; Ermanyuk, E. V.; Joubaud, Sylvain; Pillet, Grimaud; Dauxois, Thierry

2017-01-01

International audience; This paper presents an experimental study of different instability scenarios in a parallelogram-shaped internal wave attractor in a trapezoidal domain filled with a uniformly stratified fluid.Energy is injected into the system via the oscillatory motion of a vertical wall of the trapezoidal domain. Whole-field velocity measurements are performed with the conventional PIV technique. In the linear regime, the total kinetic energyof the fluid system is used to quantify th...

Low-dimensional chaotic attractors in drift wave turbulence

International Nuclear Information System (INIS)

Persson, M.; Nordman, H.

1991-01-01

Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)

Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

International Nuclear Information System (INIS)

Bucci, Francesca; Toundykov, Daniel

2010-01-01

The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

Strange Attractors in Drift Wave Turbulence

International Nuclear Information System (INIS)

Lewandowski, Jerome L.V.

2003-01-01

There are growing experimental, numerical and theoretical evidences that the anomalous transport observed in tokamaks and stellarators is caused by slow, drift-type modes (such as trapped electron modes and ion-temperature gradient-driven modes). Although typical collision frequencies in hot, magnetized fusion plasmas can be quite low in absolute values, collisional effects are nevertheless important since they act as dissipative sinks. As it is well known, dissipative systems with many (strictly speaking more than two) degrees of freedom are often chaotic and may evolve towards a so-called attractor

Regime shifts under forcing of non-stationary attractors: Conceptual model and case studies in hydrologic systems.

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Park, Jeryang; Rao, P Suresh C

2014-11-15

We present here a conceptual model and analysis of complex systems using hypothetical cases of regime shifts resulting from temporal non-stationarity in attractor strengths, and then present selected published cases to illustrate such regime shifts in hydrologic systems (shallow aquatic ecosystems; water table shifts; soil salinization). Complex systems are dynamic and can exist in two or more stable states (or regimes). Temporal variations in state variables occur in response to fluctuations in external forcing, which are modulated by interactions among internal processes. Combined effects of external forcing and non-stationary strengths of alternative attractors can lead to shifts from original to alternate regimes. In systems with bi-stable states, when the strengths of two competing attractors are constant in time, or are non-stationary but change in a linear fashion, regime shifts are found to be temporally stationary and only controlled by the characteristics of the external forcing. However, when attractor strengths change in time non-linearly or vary stochastically, regime shifts in complex systems are characterized by non-stationary probability density functions (pdfs). We briefly discuss implications and challenges to prediction and management of hydrologic complex systems. Copyright © 2014 Elsevier B.V. All rights reserved.

Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

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Danxia Wang

2015-01-01

Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l‍(ux2dxuxx-ϕ(∫0l‍(ux2dxuxxt=q(x, in  [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.

Dimension from covariance matrices.

Science.gov (United States)

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

Generation of n x m-scroll attractors in a two-port RCL network with hysteresis circuits

International Nuclear Information System (INIS)

Yu Simin; Tang, Wallace K.S.

2009-01-01

In this paper, the generation of n x m-scroll attractors based on a two-port network is presented. The two-port network is built according to the RCL circuit suggested in the conventional Chua's circuit. By appending hysteresis voltage controlled devices on this two-port network, n-scroll and n x m-scroll attractors can be duly obtained both in simulations and experiments.

Polynomial law for controlling the generation of n-scroll chaotic attractors in an optoelectronic delayed oscillator

Energy Technology Data Exchange (ETDEWEB)

Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A. [Centro de Física, Instituto Venezolano de Investigaciones Científicas, km. 11 Carretera Panamericana, Caracas 1020-A (Venezuela, Bolivarian Republic of)

2014-09-01

Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.

THE ESTIMATION OF DIMENSION AND FACTORS OF SCHOOL ABANDON

Directory of Open Access Journals (Sweden)

Andreea Iluzia IACOB

2011-12-01

Full Text Available During the transition period, in Romania, the dimension of school abandon had risen. The main goals of the study are: to estimate the school abandon rate by each educational level in Romania, to identify the factors which affect school abandon on urban and rural areas and at development regions level; to analyze the causes of earlier school abandon. In the same time, the analysis had also followed the temporal component, by including in the database the last decade statistical information. The school abandon was measured as the difference between the numbers of pupils/students found at the end of the school year and the same category enrolled at the beginning of the same year.

Hematopoietic differentiation: a coordinated dynamical process towards attractor stable states

Directory of Open Access Journals (Sweden)

Rossi Simona

2010-06-01

Full Text Available Abstract Background The differentiation process, proceeding from stem cells towards the different committed cell types, can be considered as a trajectory towards an attractor of a dynamical process. This view, taking into consideration the transcriptome and miRNome dynamics considered as a whole, instead of looking at few 'master genes' driving the system, offers a novel perspective on this phenomenon. We investigated the 'differentiation trajectories' of the hematopoietic system considering a genome-wide scenario. Results We developed serum-free liquid suspension unilineage cultures of cord blood (CB CD34+ hematopoietic progenitor cells through erythroid (E, megakaryocytic (MK, granulocytic (G and monocytic (Mo pathways. These cultures recapitulate physiological hematopoiesis, allowing the analysis of almost pure unilineage precursors starting from initial differentiation of HPCs until terminal maturation. By analyzing the expression profile of protein coding genes and microRNAs in unilineage CB E, MK, G and Mo cultures, at sequential stages of differentiation and maturation, we observed a coordinated, fully interconnected and scalable character of cell population behaviour in both transcriptome and miRNome spaces reminiscent of an attractor-like dynamics. MiRNome and transcriptome space differed for a still not terminally committed behaviour of microRNAs. Conclusions Consistent with their roles, the transcriptome system can be considered as the state space of a cell population, while the continuously evolving miRNA space corresponds to the tuning system necessary to reach the attractor. The behaviour of miRNA machinery could be of great relevance not only for the promise of reversing the differentiated state but even for tumor biology.

[A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

Science.gov (United States)

Zhonggang, Liang; Hong, Yan

2006-10-01

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

Science.gov (United States)

Ren, Shuili; Panahi, Shirin; Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Jafari, Sajad

2018-02-01

Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

Global attractors for the coupled suspension bridge system with temperature

Czech Academy of Sciences Publication Activity Database

Dell'Oro, Filippo; Giorgi, C.

2016-01-01

Roč. 39, č. 4 (2016), s. 864-875 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : absorbing set * coupled bridge system * global attractor Subject RIV: BA - General Mathematics Impact factor: 1.017, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/mma.3526/abstract

The Geometric Structure of Strange Attractors in the Lozi Map

Institute of Scientific and Technical Information of China (English)

YongluoCAO; ZengrongLIU

1998-01-01

In this paper,the structure of the strange attractors in the Lozi map is investigated on basis of the results gotten by the authors in 1991-1993,The new results of the strange atrtractors of the Lozi map show that our viewpoint is correct.

Synaptic potentiation facilitates memory-like attractor dynamics in cultured in vitro hippocampal networks.

Directory of Open Access Journals (Sweden)

Mark Niedringhaus

Full Text Available Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based computational models have been successfully implemented as a theoretical framework for memory storage in networks of neurons. Additionally, activity-dependent modification of synaptic transmission is thought to be the physiological basis of learning and memory. The goal of this study is to demonstrate that using a pharmacological treatment that has been shown to increase synaptic strength within in vitro networks of hippocampal neurons follows the dynamical postulates theorized by attractor models. We use a grid of extracellular electrodes to study changes in network activity after this perturbation and show that there is a persistent increase in overall spiking and bursting activity after treatment. This increase in activity appears to recruit more "errant" spikes into bursts. Phase plots indicate a conserved activity pattern suggesting that a synaptic potentiation perturbation to the attractor leaves it unchanged. Lastly, we construct a computational model to demonstrate that these synaptic perturbations can account for the dynamical changes seen within the network.

Turing patterns and long-time behavior in a three-species food-chain model

KAUST Repository

Parshad, Rana D.

2014-08-01

We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L2(Ω). We perform linear stability analysis and show that the model exhibits the phenomenon of Turing instability, as well as diffusion induced chaos. Various Turing patterns such as stripe patterns, mesh patterns, spot patterns, labyrinth patterns and weaving patterns are obtained, via numerical simulations in 1d as well as in 2d. The Turing and non-Turing space, in terms of model parameters, is also explored. Finally, we use methods from nonlinear time series analysis to reconstruct a low dimensional chaotic attractor of the model, and estimate its fractal dimension. This provides a lower bound, for the fractal dimension of the attractor, of the spatially explicit model. © 2014 Elsevier Inc.

Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay

Science.gov (United States)

Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao

2016-06-01

This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.

On reliability of singular-value decomposition in attractor reconstruction

International Nuclear Information System (INIS)

Palus, M.; Dvorak, I.

1990-12-01

Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs

Phase-space analysis of the cosmological 3-fluid problem: families of attractors and repellers

International Nuclear Information System (INIS)

Azreg-Aïnou, Mustapha

2013-01-01

We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter γ − 1, a pressureless dark matter fluid, plus a scalar field ϕ (representing dark energy) coupled to an exponential potential V = V 0 exp ( − κλϕ). Besides the potential–kinetic scaling solutions, which are not the unique late-time attractors whenever they exist for λ 2 ⩾ 3γ, we derive new attractors where both dark energy and dark matter coexist and the final density is shared in a way independent of the value of γ > 1. The case of a pressureless barotropic fluid (γ = 1) has a one-parameter family of attractors where all components coexist. New one-parameter families of matter–dark matter saddle points and kinetic–matter repellers exist. We investigate the stability of the ten critical points by linearization and/or Lyapunov's theorems and a variant of the theorems formulated in this paper. A solution with two transient periods of acceleration and two transient periods of deceleration is derived. (paper)

Reduction of Dietrich-Ruina attractors to unimodal maps

Directory of Open Access Journals (Sweden)

S. Shkoller

1997-01-01

Full Text Available We present a geometric analysis of a quasi-static single degree of freedom elastic slider with a state and rate dependent friction law. In particular, we examine and characterize the regime of chaotic motions displayed by the Dieterich-Ruina model. We do so by numerically reducing the chaotic attractors to a family of unimodal maps and discuss why this suggests complex behaviour in the dynamical system.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

Energy Technology Data Exchange (ETDEWEB)

Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

Science.gov (United States)

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

2013-06-01

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Estimation of Dynamic Errors in Laser Optoelectronic Dimension Gauges for Geometric Measurement of Details

Directory of Open Access Journals (Sweden)

Khasanov Zimfir

2018-01-01

Full Text Available The article reviews the capabilities and particularities of the approach to the improvement of metrological characteristics of fiber-optic pressure sensors (FOPS based on estimation estimation of dynamic errors in laser optoelectronic dimension gauges for geometric measurement of details. It is shown that the proposed criteria render new methods for conjugation of optoelectronic converters in the dimension gauge for geometric measurements in order to reduce the speed and volume requirements for the Random Access Memory (RAM of the video controller which process the signal. It is found that the lower relative error, the higher the interrogetion speed of the CCD array. It is shown that thus, the maximum achievable dynamic accuracy characteristics of the optoelectronic gauge are determined by the following conditions: the parameter stability of the electronic circuits in the CCD array and the microprocessor calculator; linearity of characteristics; error dynamics and noise in all electronic circuits of the CCD array and microprocessor calculator.

Deterministic Chaos in Radon Time Variation

International Nuclear Information System (INIS)

Planinic, J.; Vukovic, B.; Radolic, V.; Faj, Z.; Stanic, D.

2003-01-01

Radon concentrations were continuously measured outdoors, in living room and basement in 10-minute intervals for a month. The radon time series were analyzed by comparing algorithms to extract phase-space dynamical information. The application of fractal methods enabled to explore the chaotic nature of radon in the atmosphere. The computed fractal dimensions, such as Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent (λ ) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0< H<0.5) indicated anti-persistent behavior (non random changes) of the time series, but the positive values of the λ pointed out the grate sensitivity on initial conditions and appearing deterministic chaos by radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere. (author)

Radon time variations and deterministic chaos

Energy Technology Data Exchange (ETDEWEB)

Planinic, J. E-mail: planinic@pedos.hr; Vukovic, B.; Radolic, V

2004-07-01

Radon concentrations were continuously measured outdoors, in the living room and in the basement at 10 min intervals for a month. Radon time series were analyzed by comparing algorithms to extract phase space dynamical information. The application of fractal methods enabled exploration of the chaotic nature of radon in atmosphere. The computed fractal dimensions, such as the Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent ({lambda}) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere.

Radon time variations and deterministic chaos

International Nuclear Information System (INIS)

Planinic, J.; Vukovic, B.; Radolic, V.

2004-01-01

Radon concentrations were continuously measured outdoors, in the living room and in the basement at 10 min intervals for a month. Radon time series were analyzed by comparing algorithms to extract phase space dynamical information. The application of fractal methods enabled exploration of the chaotic nature of radon in atmosphere. The computed fractal dimensions, such as the Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent (λ) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0< H<0.5) indicated anti-persistent behavior (non-random changes) of the time series, but the positive values of λ pointed out the grate sensitivity on initial conditions and the deterministic chaos that appeared due to radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere

Attractor cosmology from nonminimally coupled gravity

Science.gov (United States)

Odintsov, S. D.; Oikonomou, V. K.

2018-03-01

By using a bottom-up reconstruction technique for nonminimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the Ω (ϕ )-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the nonminimal coupling Ω (ϕ ) and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the Ω (ϕ )-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the Ω (ϕ )-Jordan frame. We investigate the special conditions that are required to hold true in for this realization to occur, and we provide the analytic form of the potential in the Ω (ϕ )-Jordan frame. Also, by performing a conformal transformation, we find the corresponding Einstein frame canonical scalar-tensor theory, and we calculate in detail the corresponding observational indices. The result indicates that although the spectral index of the primordial curvature perturbations is the same in the Jordan and Einstein frames, at leading order in the e -foldings number, the scalar-to-tensor ratio differs. We discuss the possible reasons behind this discrepancy, and we argue that the difference is due to some approximation we performed to the functional form of the potential in the Einstein frame, in order to obtain analytical results, and also due to the difference in the definition of the e -foldings number in the two frames, which is also pointed out in the related literature. Finally, we find the F (R ) gravity corresponding to the Einstein frame canonical scalar-tensor theory.

The de Sitter spacetime as an attractor solution in fourth-order gravity

International Nuclear Information System (INIS)

Schmidt, H.-J.

1988-01-01

We investigate the general vacuum solution of fourth-order gravity, and include the Bach tensor. For L 2 = 1.3μR 2 + 1/2αC 2 the expanding de Sitter spacetime is an attractor in the set of axially symmetric Bianchi type-I models if and only if αμ ≤ 0 or α > 4μ holds. It will be argued that this result holds true for a large class of inhomogeneous models. As a byproduct, a new closed-form cosmological solution, is obtained. It is also shown that the de Sitter spacetime is an attractor for the Bach-Einstein gravity with a minimally coupled scalar field φ. Specialised to Einstein gravity (i.e. α = 0 above) this conformal equivalence remains a non-trivial one. (author)

Attractors of the periodically forced Rayleigh system

Directory of Open Access Journals (Sweden)

Petre Bazavan

2011-07-01

Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.

Stimulus number, duration and intensity encoding in randomly connected attractor networks with synaptic depression

Directory of Open Access Journals (Sweden)

Paul eMiller

2013-05-01

Full Text Available Randomly connected recurrent networks of excitatory groups of neurons can possess a multitude of attractor states. When the internal excitatory synapses of these networks are depressing, the attractor states can be destabilized with increasing input. This leads to an itinerancy, where with either repeated transient stimuli, or increasing duration of a single stimulus, the network activity advances through sequences of attractor states. We find that the resulting network state, which persists beyond stimulus offset, can encode the number of stimuli presented via a distributed representation of neural activity with non-monotonic tuning curves for most neurons. Increased duration of a single stimulus is encoded via different distributed representations, so unlike an integrator, the network distinguishes separate successive presentations of a short stimulus from a single presentation of a longer stimulus with equal total duration. Moreover, different amplitudes of stimulus cause new, distinct activity patterns, such that changes in stimulus number, duration and amplitude can be distinguished from each other. These properties of the network depend on dynamic depressing synapses, as they disappear if synapses are static. Thus short-term synaptic depression allows a network to store separately the different dynamic properties of a spatially constant stimulus.

Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics

Directory of Open Access Journals (Sweden)

Toichiro Asada

2011-01-01

Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.

Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''

Science.gov (United States)

Binder, Bernd

2009-03-01

In this lecture paper we derive Magic Angle Precession (MAP) from first geometric principles. MAP can arise in situations, where precession is multiply related to spin, linearly by time or distance (dynamic phase, rolling, Gauss law) and transcendentally by the holonomy loop path (geometric phase). With linear spin-precession coupling, gyroscopes can be spun up and down to very high frequencies via low frequency holonomy control induced by external accelerations, which provides for extreme coupling strengths or "anomalies" that can be tested by the powerball or gyrotwister device. Geometrically, a gyroscopic manifold with spherical metric is tangentially aligned to a precession wave channel with conic or hyperbolic metric (like the relativistic Thomas precession). Transporting triangular spin/precession vector relations across the tangential boundary of contact with SO(3) Lorentz symmetry, we get extreme vector currents near the attractor fixed points in precession phase space, where spin currents remain intact while crossing the contact boundaries between regions of different curvature signature (-1, 0, +1). The problem can be geometrically solved by considering a curvature invariant triangular condition, which holds on surfaces with different curvature that are in contact and locally parallel. In this case two out of three angles are identical, whereas the third angle is different due to holonomy. If we require that the side length ratio corresponding to these angles are invariant we get a geodesic chaotic attractor, which is a cosine map cos(x)˜Mx in parameter space providing for fixed points, limit cycle bifurcations, and singularities. The situation could be quite natural and common in the context of vector currents in curved spacetime and gauge theories. MAP could even be part of the electromagnetic interaction, where the electric charge is the geometric U(1) precession spin current and gauge potential with magnetic effects given by extra rotations under the

Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research

NARCIS (Netherlands)

Golino, H.F.; Epskamp, S.

2017-01-01

The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman’s eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use

Neural attractor network for application in visual field data classification

International Nuclear Information System (INIS)

Fink, Wolfgang

2004-01-01

The purpose was to introduce a novel method for computer-based classification of visual field data derived from perimetric examination, that may act as a ' counsellor', providing an independent 'second opinion' to the diagnosing physician. The classification system consists of a Hopfield-type neural attractor network that obtains its input data from perimetric examination results. An iterative relaxation process determines the states of the neurons dynamically. Therefore, even 'noisy' perimetric output, e.g., early stages of a disease, may eventually be classified correctly according to the predefined idealized visual field defect (scotoma) patterns, stored as attractors of the network, that are found with diseases of the eye, optic nerve and the central nervous system. Preliminary tests of the classification system on real visual field data derived from perimetric examinations have shown a classification success of over 80%. Some of the main advantages of the Hopfield-attractor-network-based approach over feed-forward type neural networks are: (1) network architecture is defined by the classification problem; (2) no training is required to determine the neural coupling strengths; (3) assignment of an auto-diagnosis confidence level is possible by means of an overlap parameter and the Hamming distance. In conclusion, the novel method for computer-based classification of visual field data, presented here, furnishes a valuable first overview and an independent 'second opinion' in judging perimetric examination results, pointing towards a final diagnosis by a physician. It should not be considered a substitute for the diagnosing physician. Thanks to the worldwide accessibility of the Internet, the classification system offers a promising perspective towards modern computer-assisted diagnosis in both medicine and tele-medicine, for example and in particular, with respect to non-ophthalmic clinics or in communities where perimetric expertise is not readily available

Pullback attractors for three-dimensional non-autonomous Navier–Stokes–Voigt equations

International Nuclear Information System (INIS)

García-Luengo, Julia; Marín-Rubio, Pedro; Real, José

2012-01-01

In this paper, we consider a non-autonomous Navier–Stokes–Voigt model, with which a continuous process can be associated. We study the existence and relationship between minimal pullback attractors for this process in two different frameworks, namely, for the universe of fixed bounded sets, and also for another universe given by a tempered condition. Since the model does not have a regularizing effect, obtaining asymptotic compactness for the process is a more involved task. We prove this in a relatively simple way just using an energy method. Our results simplify—and in some aspects generalize—some of those obtained previously for the autonomous and non-autonomous cases, since for example in section 4, regularity is not required for the boundary of the domain and the force may take values in V'. Under additional suitable assumptions, regularity results for these families of attractors are also obtained, via bootstrapping arguments. Finally, we also conclude some results concerning the attraction in the D(A) norm

Structural health monitoring based on sensitivity vector fields and attractor morphing.

Science.gov (United States)

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

Energy Technology Data Exchange (ETDEWEB)

Cid, Antonella [Grupo de Cosmología y Gravitación GCG-UBB and Departamento de Física, Universidad del Bío-Bío, Casilla 5-C, Concepción (Chile); Leon, Genly [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Leyva, Yoelsy, E-mail: acidm@ubiobio.cl, E-mail: genly.leon@ucv.cl, E-mail: yoelsy.leyva@uta.cl [Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Casilla 7-D, Arica (Chile)

2016-02-01

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, φ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field φ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. We prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 1} t{sup p{sup {sub 1}}}}, as t → ∞ where α{sub 1} > 0 and 0 < p{sub 1} < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 2} tp{sub 2}} as t → ∞ where α{sub 2} > 0 and 0attractor is linked with the exact solution found for the induced gravity model. In this example the ''intermediate accelerated

Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

International Nuclear Information System (INIS)

Cid, Antonella; Leon, Genly; Leyva, Yoelsy

2016-01-01

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, φ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field φ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. We prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ''intermediate accelerated'' solution of the form a(t) ≅ e α 1  t p 1 , as t → ∞ where α 1  > 0 and 0 < p 1  < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ''intermediate accelerated'' solution of the form a(t) ≅ e α 2  tp 2 as t → ∞ where α 2  > 0 and 0

attractor is linked with the exact solution found for the induced gravity model. In this example the ''intermediate accelerated'' solution does not exist, and the attractor

Global dynamics of a PDE model for aedes aegypti mosquitoe incorporating female sexual preference

KAUST Repository

Parshad, Rana

2011-01-01

In this paper we study the long time dynamics of a reaction diffusion system, describing the spread of Aedes aegypti mosquitoes, which are the primary cause of dengue infection. The system incorporates a control attempt via the sterile insect technique. The model incorporates female mosquitoes sexual preference for wild males over sterile males. We show global existence of strong solution for the system. We then derive uniform estimates to prove the existence of a global attractor in L-2(Omega), for the system. The attractor is shown to be L-infinity(Omega) regular and posess state of extinction, if the injection of sterile males is large enough. We also provide upper bounds on the Hausdorff and fractal dimensions of the attractor.

New explicit spike solutions-non-local component of the generalized Mixmaster attractor

International Nuclear Information System (INIS)

Lim, Woei Chet

2008-01-01

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solutions are part of the generalized Mixmaster attractor

Long time behavior and attractors for energetically insulated fluid systems

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2010-01-01

Roč. 27, č. 4 (2010), s. 1587-1609 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier system * attractor * long time behavior Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5040

Pullback attractors for a singularly nonautonomous plate equation

Directory of Open Access Journals (Sweden)

Vera Lucia Carbone

2011-06-01

Full Text Available We consider the family of singularly nonautonomous plate equations with structural damping $$ u_{tt} + a(t,xu_t - Delta u_t + (-Delta^2 u + lambda u = f(u, $$ in a bounded domain $Omega subset mathbb{R}^n$, with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in $H^2_0(Omega imes L^2(Omega$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

Emergence of unstable itinerant orbits in a recurrent neural network model

International Nuclear Information System (INIS)

Suemitsu, Yoshikazu; Nara, Shigetoshi

2005-01-01

A recurrent neural network model with time delay is investigated by numerical methods. The model functions as both conventional associative memory and also enables us to embed a new kind of memory attractor that cannot be realized in models without time delay, for example chain-ring attractors. This is attributed to the fact that the time delay extends the available state space dimension. The difference between the basin structures of chain-ring attractors and of isolated cycle attractors is investigated with respect to the two attractor pattern sets, random memory patterns and designed memory patterns with intended structures. Compared to isolated attractors with random memory patterns, the basins of chain-ring attractors are reduced considerably. Computer experiments confirm that the basin volume of each embedded chain-ring attractor shrinks and the emergence of unstable itinerant orbits in the outer state space of the memory attractor basins is discovered. The instability of such itinerant orbits is investigated. Results show that a 1-bit difference in initial conditions does not exceed 10% of a total dimension within 100 updating steps

AHaH Computing–From Metastable Switches to Attractors to Machine Learning

Science.gov (United States)

Nugent, Michael Alexander; Molter, Timothy Wesley

2014-01-01

Modern computing architecture based on the separation of memory and processing leads to a well known problem called the von Neumann bottleneck, a restrictive limit on the data bandwidth between CPU and RAM. This paper introduces a new approach to computing we call AHaH computing where memory and processing are combined. The idea is based on the attractor dynamics of volatile dissipative electronics inspired by biological systems, presenting an attractive alternative architecture that is able to adapt, self-repair, and learn from interactions with the environment. We envision that both von Neumann and AHaH computing architectures will operate together on the same machine, but that the AHaH computing processor may reduce the power consumption and processing time for certain adaptive learning tasks by orders of magnitude. The paper begins by drawing a connection between the properties of volatility, thermodynamics, and Anti-Hebbian and Hebbian (AHaH) plasticity. We show how AHaH synaptic plasticity leads to attractor states that extract the independent components of applied data streams and how they form a computationally complete set of logic functions. After introducing a general memristive device model based on collections of metastable switches, we show how adaptive synaptic weights can be formed from differential pairs of incremental memristors. We also disclose how arrays of synaptic weights can be used to build a neural node circuit operating AHaH plasticity. By configuring the attractor states of the AHaH node in different ways, high level machine learning functions are demonstrated. This includes unsupervised clustering, supervised and unsupervised classification, complex signal prediction, unsupervised robotic actuation and combinatorial optimization of procedures–all key capabilities of biological nervous systems and modern machine learning algorithms with real world application. PMID:24520315

AHaH computing-from metastable switches to attractors to machine learning.

Directory of Open Access Journals (Sweden)

Michael Alexander Nugent

Full Text Available Modern computing architecture based on the separation of memory and processing leads to a well known problem called the von Neumann bottleneck, a restrictive limit on the data bandwidth between CPU and RAM. This paper introduces a new approach to computing we call AHaH computing where memory and processing are combined. The idea is based on the attractor dynamics of volatile dissipative electronics inspired by biological systems, presenting an attractive alternative architecture that is able to adapt, self-repair, and learn from interactions with the environment. We envision that both von Neumann and AHaH computing architectures will operate together on the same machine, but that the AHaH computing processor may reduce the power consumption and processing time for certain adaptive learning tasks by orders of magnitude. The paper begins by drawing a connection between the properties of volatility, thermodynamics, and Anti-Hebbian and Hebbian (AHaH plasticity. We show how AHaH synaptic plasticity leads to attractor states that extract the independent components of applied data streams and how they form a computationally complete set of logic functions. After introducing a general memristive device model based on collections of metastable switches, we show how adaptive synaptic weights can be formed from differential pairs of incremental memristors. We also disclose how arrays of synaptic weights can be used to build a neural node circuit operating AHaH plasticity. By configuring the attractor states of the AHaH node in different ways, high level machine learning functions are demonstrated. This includes unsupervised clustering, supervised and unsupervised classification, complex signal prediction, unsupervised robotic actuation and combinatorial optimization of procedures-all key capabilities of biological nervous systems and modern machine learning algorithms with real world application.

Nonlinear attractor dynamics in the fundamental and extended prism adaptation paradigm

International Nuclear Information System (INIS)

Frank, T.D.; Blau, Julia J.C.; Turvey, M.T.

2009-01-01

Adaptation and re-adaptation processes are studied in terms of dynamic attractors that evolve and devolve. In doing so, a theoretical account is given for the fundamental observation that adaptation and re-adaptation processes do not exhibit one-trial learning. Moreover, the emergence of the latent aftereffect in the extended prism paradigm is addressed

A parallel attractor-finding algorithm based on Boolean satisfiability for genetic regulatory networks.

Directory of Open Access Journals (Sweden)

Wensheng Guo

Full Text Available In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.

Linear-control-based synchronization of coexisting attractor networks with time delays

International Nuclear Information System (INIS)

Yun-Zhong, Song

2010-01-01

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, but also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme. (general)

Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay

NARCIS (Netherlands)

Broer, Hendrik; Efstathiou, Konstantinos; Subramanian, Easwar

We consider arbitrarily large networks of pulse-coupled oscillators with non-zero delay where the coupling is given by the Mirollo-Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for

Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit

Energy Technology Data Exchange (ETDEWEB)

Kengne, J. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.; Nguomkam Negou, A. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Department of Physics, Laboratory of Electronics and Signal Processing (LETS), Faculty of Science, University of Dschang, Dschang (Cameroon)

2015-10-15

In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.

?Strange Attractors (chaos) in the hydro-climatology of Colombia?

International Nuclear Information System (INIS)

Poveda Jaramillo, German

1997-01-01

Inter annual hydro-climatology of Colombia is strongly influenced by extreme phases of ENSO, a phenomenon exhibiting many features of chaotic non-linear system. The possible chaotic nature of Colombian hydrology is examined by using time series of monthly precipitation at Bogota (1866-1992) and Medellin (1908-1995), and average stream flows of the Magdalena River at Puerto Berrio. The power spectrum, the Haussdorf-Besikovich (fractal) dimension, the correlation dimension, and the largest Lyapunov exponent are estimated for the time series. Ideas of hydrologic forecasting and predictability are discussed in the context of nonlinear dynamical systems exhibit chaotic behavior

Multiplication factor versus regression analysis in stature estimation from hand and foot dimensions.

Science.gov (United States)

Krishan, Kewal; Kanchan, Tanuj; Sharma, Abhilasha

2012-05-01

Estimation of stature is an important parameter in identification of human remains in forensic examinations. The present study is aimed to compare the reliability and accuracy of stature estimation and to demonstrate the variability in estimated stature and actual stature using multiplication factor and regression analysis methods. The study is based on a sample of 246 subjects (123 males and 123 females) from North India aged between 17 and 20 years. Four anthropometric measurements; hand length, hand breadth, foot length and foot breadth taken on the left side in each subject were included in the study. Stature was measured using standard anthropometric techniques. Multiplication factors were calculated and linear regression models were derived for estimation of stature from hand and foot dimensions. Derived multiplication factors and regression formula were applied to the hand and foot measurements in the study sample. The estimated stature from the multiplication factors and regression analysis was compared with the actual stature to find the error in estimated stature. The results indicate that the range of error in estimation of stature from regression analysis method is less than that of multiplication factor method thus, confirming that the regression analysis method is better than multiplication factor analysis in stature estimation. Copyright © 2012 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Random Attractors for the Stochastic Navier-Stokes Equations on the 2D Unit Sphere

Science.gov (United States)

Brzeźniak, Z.; Goldys, B.; Le Gia, Q. T.

2018-03-01

In this paper we prove the existence of random attractors for the Navier-Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.

Supersymmetry, attractors and cosmic censorship

Energy Technology Data Exchange (ETDEWEB)

Bellorin, Jorge [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: jorge.bellorin@uam.es; Meessen, Patrick [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: patrick.meessen@cern.ch; Ortin, Tomas [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: tomas.ortin@cern.ch

2007-01-29

We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N=2, d=4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We formulate three specific conditions which we argue are equivalent to the requirement of global supersymmetry. These three conditions can be related to the absence of sources for NUT charge, angular momentum, scalar hair and negative energy, although the solutions can still have globally defined angular momentum and non-trivial scalar fields, as we show in an explicit example. Furthermore, only the solutions satisfying these requirements seem to have a microscopic interpretation in string theory since only they have supersymmetric sources. These conditions exclude, for instance, singular solutions such as the Kerr-Newman with M=|q|, which fails to be everywhere supersymmetric. We also present a re-derivation of several results concerning attractors in N=2, d=4 theories based on the explicit knowledge of the most general solutions in the timelike class.

Some statistical properties of strange attractors: engineering view

International Nuclear Information System (INIS)

Mijangos, M; Kontorovich, V; Aguilar-Torrentera, J

2008-01-01

In this paper, the statistical characterization of strange attractors is investigated via the so-called 'model distribution' approach. It is shown that in order to calculate the first four cumulants, which are necessary to create a model distribution of kurtosis approximation, a systematic method for the calculus of the variance needs to be considered. Correspondently, an analytical method based on the Kolmogorov-Sinai (K-S) entropy for variance approximation is herein proposed. The methodology is of interest for its application in the statistical analysis of chaotic systems that model physical phenomena found in some areas of electrical (communication) engineering

Dynamics of neural networks with continuous attractors

Science.gov (United States)

Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si

2008-10-01

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.

Plykin type attractor in electronic device simulated in MULTISIM

Science.gov (United States)

Kuznetsov, Sergey P.

2011-12-01

An electronic device is suggested representing a non-autonomous dynamical system with hyperbolic chaotic attractor of Plykin type in the stroboscopic map, and the results of its simulation with software package NI MULTISIM are considered in comparison with numerical integration of the underlying differential equations. A main practical advantage of electronic devices of this kind is their structural stability that means insensitivity of the chaotic dynamics in respect to variations of functions and parameters of elements constituting the system as well as to interferences and noises.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

International Nuclear Information System (INIS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

2016-01-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Identification of core pathways based on attractor and crosstalk in ischemic stroke.

Science.gov (United States)

Diao, Xiufang; Liu, Aijuan

2018-02-01

Ischemic stroke is a leading cause of mortality and disability around the world. It is an important task to identify dysregulated pathways which infer molecular and functional insights existing in high-throughput experimental data. Gene expression profile of E-GEOD-16561 was collected. Pathways were obtained from the database of Kyoto Encyclopedia of Genes and Genomes and Retrieval of Interacting Genes was used to download protein-protein interaction sets. Attractor and crosstalk approaches were applied to screen dysregulated pathways. A total of 20 differentially expressed genes were identified in ischemic stroke. Thirty-nine significant differential pathways were identified according to Ppathways were identified with RPpathways were identified with impact factor >250. On the basis of the three criteria, 11 significant dysfunctional pathways were identified. Among them, Epstein-Barr virus infection was the most significant differential pathway. In conclusion, with the method based on attractor and crosstalk, significantly dysfunctional pathways were identified. These pathways are expected to provide molecular mechanism of ischemic stroke and represents a novel potential therapeutic target for ischemic stroke treatment.

Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity

Energy Technology Data Exchange (ETDEWEB)

Hristov, Kiril [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia (Bulgaria); Katmadas, Stefanos [Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,I-20126 Milano (Italy); Lodato, Ivano [Department of Physics, IISER Pune,Homi Bhaba Road, Pashan, Pune (India)

2016-05-30

We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS{sub 2}×S{sup 2} (or other Riemann surface) preserves half of the supercharges in N=2 supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending on the model, the attractors are part of full black hole solutions with different asymptotics, such as Minkowski, AdS{sub 4}, and hvLif{sub 4}. We give explicit examples for each of the asymptotic cases and comment on the implications. Among other results, we find that the Weyl-squared terms spoil the exact two-derivative relation to non-BPS asymptotically flat black holes in ungauged supergravity.

Attractor States in Teaching and Learning Processes: A Study of Out-of-School Science Education.

Science.gov (United States)

Geveke, Carla H; Steenbeek, Henderien W; Doornenbal, Jeannette M; Van Geert, Paul L C

2017-01-01

In order for out-of-school science activities that take place during school hours but outside the school context to be successful, instructors must have sufficient pedagogical content knowledge (PCK) to guarantee high-quality teaching and learning. We argue that PCK is a quality of the instructor-pupil system that is constructed in real-time interaction. When PCK is evident in real-time interaction, we define it as Expressed Pedagogical Content Knowledge (EPCK). The aim of this study is to empirically explore whether EPCK shows a systematic pattern of variation, and if so whether the pattern occurs in recurrent and temporary stable attractor states as predicted in the complex dynamic systems theory. This study concerned nine out-of-school activities in which pupils of upper primary school classes participated. A multivariate coding scheme was used to capture EPCK in real time. A principal component analysis of the time series of all the variables reduced the number of components. A cluster revealed general descriptions of the components across all cases. Cluster analyses of individual cases divided the time series into sequences, revealing High-, Low-, and Non-EPCK states. High-EPCK attractor states emerged at particular moments during activities, rather than being present all the time. Such High-EPCK attractor states were only found in a few cases, namely those where the pupils were prepared for the visit and the instructors were trained.

Reconstructing a f ( R ) theory from the α-Attractors

Energy Technology Data Exchange (ETDEWEB)

Miranda, T.; Fabris, J. C.; Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br [Department of Physics, Universidade Federal do Espírito Santo, avenida Fernando Ferrari 514, 29075-910 Vitória, Espírito Santo (Brazil)

2017-09-01

We show an analogy at high curvature between a f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} theory and the α-Attractors. We calculate the expressions of the parameters a , b and n as functions of α and the predictions of the model f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r . We find that the power law correction R {sup n} {sup −} {sup 1} allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on n {sub s}. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2}. Moreover, we also investigate the case of a single power law f ( R ) = γ R {sup 2} {sup −} {sup δ} theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015 < δ < 0.016, confirming once again the excellent agreement between the Starobinsky model and observation.

Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise

Directory of Open Access Journals (Sweden)

Hongyan Li

2015-10-01

Full Text Available In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.

Coupled flare attractors – a discrete prototype for economic modelling

Directory of Open Access Journals (Sweden)

Georg C. Hartmann

1999-01-01

Full Text Available A chaotic environment can give rise to “flares” if an autocatalytic variable responds in a multiplicative, threshold-type fashion to the environmental forcing. An “economic unit” similarly depends in its growth behavior on the unpredictable (chaotic? buying habits of its customers, say. It turns out that coupled flare attractors are surprisingly robust in the sense that the resulting “economy” is largely independent of the extent of diffusive coupling used. Some simulations are presented.

Spreading Activation in an Attractor Network with Latching Dynamics: Automatic Semantic Priming Revisited

Science.gov (United States)

Lerner, Itamar; Bentin, Shlomo; Shriki, Oren

2012-01-01

Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified…

Black hole microstates and attractor without supersymmetry

International Nuclear Information System (INIS)

Dabholkar, Atish; Trivedi, Sandip P.; Sen, Ashoke

2007-01-01

Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously as we vary the asymptotic values of various moduli fields. Using this fact we argue that the entropy of an extremal black hole in string theory, calculated for a range of values of the asymptotic moduli for which the microscopic theory is strongly coupled, should match the statistical entropy of the same system calculated for a range of values of the asymptotic moduli for which the microscopic theory is weakly coupled. This argument does not rely on supersymmetry and applies equally well to nonsupersymmetric extremal black holes. We discuss several examples which support this argument and also several caveats which could invalidate this argument

6d → 5d → 4d reduction of BPS attractors in flat gauged supergravities

Directory of Open Access Journals (Sweden)

Kiril Hristov

2015-08-01

This is achieved starting from the BPS black string in 6d with an AdS3×S3 attractor and taking two different routes to arrive at a 1/2 BPS AdS2×S2 attractor of a non-BPS black hole in 4d N=2 flat gauged supergravity. The two inequivalent routes interchange the order of KK reduction on AdS3 and SS reduction on S3. We also find the commutator between the two operations after performing a duality transformation: on the level of the theory the result is the exchange of electric with magnetic gaugings; on the level of the solution we find a flip of the quartic invariant I4 to −I4.

Quintessential inflation with α-attractors

Energy Technology Data Exchange (ETDEWEB)

Dimopoulos, Konstantinos; Owen, Charlotte, E-mail: k.dimopoulos1@lancaster.ac.uk, E-mail: c.owen@lancaster.ac.uk [Consortium for Fundamental Physics, Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom)

2017-06-01

A novel approach to quintessential inflation model building is studied, within the framework of α-attractors, motivated by supergravity theories. Inflationary observables are in excellent agreement with the latest CMB observations, while quintessence explains the dark energy observations without any fine-tuning. The model is kept intentionally minimal, avoiding the introduction of many degrees of freedom, couplings and mass scales. In stark contrast to ΛCDM, for natural values of the parameters, the model attains transient accelerated expansion, which avoids the future horizon problem, while it maintains the field displacement mildly sub-Planckian such that the flatness of the quintessential tail is not lifted by radiative corrections and violations of the equivalence principle (fifth force) are under control. In particular, the required value of the cosmological constant is near the eletroweak scale. Attention is paid to the reheating of the Universe, which avoids gravitino overproduction and respects nucleosynthesis constraints. Kination is treated in a model independent way. A spike in gravitational waves, due to kination, is found not to disturb nucleosynthesis as well.

The dynamical and statistical properties of cognitive strategies: relations between strategies, attractors, and latent classes

NARCIS (Netherlands)

van der Maas, H.L.J.; Newell, K.; Molenaar, P.C.M.

1998-01-01

Cognitive developmental psychology is faced with new developments in the mathematical theory of nonlinear dynamic systems and in psychometrics. This chapter addresses: the relation between the strategy concept in cognitive developmental psychology and the concept of attractor in nonlinear dynamic

Improving the Curie depth estimation through optimizing the spectral block dimensions of the aeromagnetic data in the Sabalan geothermal field

Science.gov (United States)

Akbar, Somaieh; Fathianpour, Nader

2016-12-01

The Curie point depth is of great importance in characterizing geothermal resources. In this study, the Curie iso-depth map was provided using the well-known method of dividing the aeromagnetic dataset into overlapping blocks and analyzing the power spectral density of each block separately. Determining the optimum block dimension is vital in improving the resolution and accuracy of estimating Curie point depth. To investigate the relation between the optimal block size and power spectral density, a forward magnetic modeling was implemented on an artificial prismatic body with specified characteristics. The top, centroid, and bottom depths of the body were estimated by the spectral analysis method for different block dimensions. The result showed that the optimal block size could be considered as the smallest possible block size whose corresponding power spectrum represents an absolute maximum in small wavenumbers. The Curie depth map of the Sabalan geothermal field and its surrounding areas, in the northwestern Iran, was produced using a grid of 37 blocks with different dimensions from 10 × 10 to 50 × 50 km2, which showed at least 50% overlapping with adjacent blocks. The Curie point depth was estimated in the range of 5 to 21 km. The promising areas with the Curie point depths less than 8.5 km are located around Mountain Sabalan encompassing more than 90% of known geothermal resources in the study area. Moreover, the Curie point depth estimated by the improved spectral analysis is in good agreement with the depth calculated from the thermal gradient data measured in one of the exploratory wells in the region.

Topology and computational performance of attractor neural networks

International Nuclear Information System (INIS)

McGraw, Patrick N.; Menzinger, Michael

2003-01-01

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world, and scale-free topologies. The random configuration is the most efficient for storage and retrieval of patterns by the network as a whole. However, in the scale-free case retrieval errors are not distributed uniformly among the nodes. The portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. The implications of these findings for brain function and social dynamics are suggestive

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems.

Science.gov (United States)

Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias

2014-01-01

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

Science.gov (United States)

Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias

2014-02-01

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

Science.gov (United States)

Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2017-12-01

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.

Attractors, statefinders and observational measurement for chameleonic Brans-Dicke cosmology

Energy Technology Data Exchange (ETDEWEB)

Farajollahi, Hossein; Salehi, Amin, E-mail: hosseinf@guilan.ac.ir, E-mail: a.salehi@guilan.ac.ir [Department of Physics, University of Guilan, Rasht (Iran, Islamic Republic of)

2010-11-01

We investigate chameleonic Brans-Dicke model applied to the FRW universes. A framework to study stability and attractor solutions in the phase space is developed for the model. We show that depending on the matter field and stability conditions, it is possible to realize phantom-like behavior without introducing phantom filed in the model while the stability is fulfilled and phantom crossing occurs. The statefinder parameters to the model for different kinds of matter interacting with the chameleon scalar field are studied. We also compare our model with present day observations.

Attractors, statefinders and observational measurement for chameleonic Brans-Dicke cosmology

International Nuclear Information System (INIS)

Farajollahi, Hossein; Salehi, Amin

2010-01-01

We investigate chameleonic Brans-Dicke model applied to the FRW universes. A framework to study stability and attractor solutions in the phase space is developed for the model. We show that depending on the matter field and stability conditions, it is possible to realize phantom-like behavior without introducing phantom filed in the model while the stability is fulfilled and phantom crossing occurs. The statefinder parameters to the model for different kinds of matter interacting with the chameleon scalar field are studied. We also compare our model with present day observations

Multistability and hidden attractors in a relay system with hysteresis

DEFF Research Database (Denmark)

Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.

2015-01-01

with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values...... of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations. (C) 2015 Elsevier B.V. All rights reserved....

The topology of chaos Alice in stretch and squeezeland

CERN Document Server

Gilmore, Robert

2002-01-01

A new approach to understanding nonlinear dynamics and strange attractors. The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question

How organisms do the right thing: The attractor hypothesis

Science.gov (United States)

Emlen, J.M.; Freeman, D.C.; Mills, A.; Graham, J.H.

1998-01-01

Neo-Darwinian theory is highly successful at explaining the emergence of adaptive traits over successive generations. However, there are reasons to doubt its efficacy in explaining the observed, impressively detailed adaptive responses of organisms to day-to-day changes in their surroundings. Also, the theory lacks a clear mechanism to account for both plasticity and canalization. In effect, there is a growing sentiment that the neo-Darwinian paradigm is incomplete, that something more than genetic structure, mutation, genetic drift, and the action of natural selection is required to explain organismal behavior. In this paper we extend the view of organisms as complex self-organizing entities by arguing that basic physical laws, coupled with the acquisitive nature of organisms, makes adaptation all but tautological. That is, much adaptation is an unavoidable emergent property of organisms' complexity and, to some a significant degree, occurs quite independently of genomic changes wrought by natural selection. For reasons that will become obvious, we refer to this assertion as the attractor hypothesis. The arguments also clarify the concept of "adaptation." Adaptation across generations, by natural selection, equates to the (game theoretic) maximization of fitness (the success with which one individual produces more individuals), while self-organizing based adaptation, within generations, equates to energetic efficiency and the matching of intake and biosynthesis to need. Finally, we discuss implications of the attractor hypothesis for a wide variety of genetical and physiological phenomena, including genetic architecture, directed mutation, genetic imprinting, paramutation, hormesis, plasticity, optimality theory, genotype-phenotype linkage and puncuated equilibrium, and present suggestions for tests of the hypothesis. ?? 1998 American Institute of Physics.

Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay

International Nuclear Information System (INIS)

Broer, Henk; Efstathiou, Konstantinos; Subramanian, Easwar

2008-01-01

We consider arbitrarily large networks of pulse-coupled oscillators with non-zero delay where the coupling is given by the Mirollo–Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for three or more oscillators. The evolution operator of the system can be discontinuous and we propose an improved model with continuous evolution operator

Solving Stochastic Büchi Games on Infinite Arenas with a Finite Attractor

Directory of Open Access Journals (Sweden)

Nathalie Bertrand

2013-06-01

Full Text Available We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized Büchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and associated winning strategies in the case where the arena satisfies the finite-attractor property. From this we directly deduce the decidability of these games on probabilistic lossy channel systems.

Attractor Structures of Signaling Networks: Consequences of Different Conformational Barcode Dynamics and Their Relations to Network-Based Drug Design.

Science.gov (United States)

Szalay, Kristóf Z; Nussinov, Ruth; Csermely, Peter

2014-06-01

Conformational barcodes tag functional sites of proteins and are decoded by interacting molecules transmitting the incoming signal. Conformational barcodes are modified by all co-occurring allosteric events induced by post-translational modifications, pathogen, drug binding, etc. We argue that fuzziness (plasticity) of conformational barcodes may be increased by disordered protein structures, by integrative plasticity of multi-phosphorylation events, by increased intracellular water content (decreased molecular crowding) and by increased action of molecular chaperones. This leads to increased plasticity of signaling and cellular networks. Increased plasticity is both substantiated by and inducing an increased noise level. Using the versatile network dynamics tool, Turbine (www.turbine.linkgroup.hu), here we show that the 10 % noise level expected in cellular systems shifts a cancer-related signaling network of human cells from its proliferative attractors to its largest, apoptotic attractor representing their health-preserving response in the carcinogen containing and tumor suppressor deficient environment modeled in our study. Thus, fuzzy conformational barcodes may not only make the cellular system more plastic, and therefore more adaptable, but may also stabilize the complex system allowing better access to its largest attractor. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

STRANGE ATTRACTORS IN SYMMETRIC UNFOLDINGS OF A SINGULARITY WITH THREE-FOLD ZERO EIGENVALUE

Institute of Scientific and Technical Information of China (English)

Qinghua Zhou

2009-01-01

In this paper, we study the Sil'nikov heteroclinic bifurcations, which display strange attractors, for the symmetric versal unfoldings of the singularity at the origin with a nilpotent Linear part and 3-jet, using the normal form, the blow-up and the ge-neralized Mel'nikov methods of heteroclinic orbits to two hyperbolic or nonhyperbolic equilibria in a high-dimensional space.

Generalized pole inflation: Hilltop, natural, and chaotic inflationary attractors

Energy Technology Data Exchange (ETDEWEB)

Terada, Takahiro, E-mail: takahiro.terada@apctp.org [Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan); Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of)

2016-09-10

A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor behaviors of these models and compute corrections from the additional poles to the inflationary observables.

Bump formation in a binary attractor neural network

International Nuclear Information System (INIS)

Koroutchev, Kostadin; Korutcheva, Elka

2006-01-01

The conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity are investigated. We show that these formations are observed when asymmetry between the activity during the retrieval and learning is imposed. An analytical approximation for the order parameters is derived. The corresponding phase diagram shows a relatively large and stable region where this effect is observed, although critical storage and information capacities drastically decrease inside that region. We demonstrate that the stability of the network, when starting from the bump formation, is larger than the stability when starting even from the whole pattern. Finally, we show a very good agreement between the analytical results and the simulations performed for different topologies of the network

Strange attractor of Henon map and its basin

Institute of Scientific and Technical Information of China (English)

曹永罗

1995-01-01

In this paper, Henon map is considered. For a positive measure set of parameters (a, b), we construct a trapping region G of topologically transitive strange attractor Aa,b for Ta,b, and prove that Aa,b= ∩n≥0Ta,bnG, and the basin B(Aa,b) of Aa,b is exactly the union of domain whose boundary is contained in w5(p) ∪wu(p) and ws(p). Therefore, that the conjecture posed by Benedicks and Carleson about the basin of strange attactor is true is proved. Furthermore, B(Aa,b) is simply connected and path-connected, w4(p2) is contained in the attainable boundary set of B(Aa,b) (where p2 is another hyperbolic fixed point of Ta,b).

Birth of new folds and competing attractors in Elmo Bumpy Torus

Energy Technology Data Exchange (ETDEWEB)

Punjabi, A; Vahala, G

1984-04-09

The topology of equilibrium surfaces for the point model equations with neoclassical nonresonant ions in EBT is a complicated nongradient-dynamic version of the canonical cusp catastrophe. New folds emerge from degenerate equilibrium surfaces as the control vector (filling pressure, microwave power, ambipolar potential) is changed. Strong sensitivity to small changes in initial conditions of the state variables (electron/ion temperatures, plasma density) is found that can drastically alter the final equilibrium state when competing point attractors are present. 5 references, 3 figures.

Distortions in recall from visual memory: two classes of attractors at work.

Science.gov (United States)

Huang, Jie; Sekuler, Robert

2010-02-24

In a trio of experiments, a matching procedure generated direct, analogue measures of short-term memory for the spatial frequency of Gabor stimuli. Experiment 1 showed that when just a single Gabor was presented for study, a retention interval of just a few seconds was enough to increase the variability of matches, suggesting that noise in memory substantially exceeds that in vision. Experiment 2 revealed that when a pair of Gabors was presented on each trial, the remembered appearance of one of the Gabors was influenced by: (1) the relationship between its spatial frequency and the spatial frequency of the accompanying, task-irrelevant non-target stimulus; and (2) the average spatial frequency of Gabors seen on previous trials. These two influences, which work on very different time scales, were approximately additive in their effects, each operating as an attractor for remembered appearance. Experiment 3 showed that a timely pre-stimulus cue allowed selective attention to curtail the influence of a task-irrelevant non-target, without diminishing the impact of the stimuli seen on previous trials. It appears that these two separable attractors influence distinct processes, with perception being influenced by the non-target stimulus and memory being influenced by stimuli seen on previous trials.

The Kuramoto–Sivashinsky equation. A Local Attractor Filled with Unstable Periodic Solutions

Directory of Open Access Journals (Sweden)

Anatoli N. Kulikov

2018-01-01

Full Text Available A periodic boundary value problem is considered for one version of the KuramotoSivashinsky equation, which is widely known in mathematical physics. Local bifurcations in a neighborhood of the spatially homogeneous equilibrium points in the case when they change stability are studied. It is shown that the loss of stability of homogeneous equilibrium points leads to the appearance of a two-dimensional attractor on which all solutions are periodic functions of time, except one spatially inhomogeneous state. A spectrum of frequencies of the given family of periodic solutions fills the entire number line, and they are all unstable in a sense of Lyapunov definition in the metric of the phase space (space of initial conditions of the corresponding initial boundary value problem. It is chosen the Sobolev space as the phase space. For the periodic solutions which fill the two-dimensional attractor, the asymptotic formulas are given. In order to analyze the bifurcation problem it was used analysis methods for infinite-dimensional dynamical systems: the integral (invariant manifold method, the Poincare normal form theory, and asymptotic methods. The analysis of bifurcations for periodic boundary value problem was reduced to analysing the structure of the neighborhood of the zero solution of the homogeneous Dirichlet boundary value problem for the considered equation. 

Defeat and entrapment: more than meets the eye? Applying network analysis to estimate dimensions of highly correlated constructs.

Science.gov (United States)

Forkmann, Thomas; Teismann, Tobias; Stenzel, Jana-Sophie; Glaesmer, Heide; de Beurs, Derek

2018-01-25

Defeat and entrapment have been shown to be of central relevance to the development of different disorders. However, it remains unclear whether they represent two distinct constructs or one overall latent variable. One reason for the unclarity is that traditional factor analytic techniques have trouble estimating the right number of clusters in highly correlated data. In this study, we applied a novel approach based on network analysis that can deal with correlated data to establish whether defeat and entrapment are best thought of as one or multiple constructs. Explanatory graph analysis was used to estimate the number of dimensions within the 32 items that make up the defeat and entrapment scales in two samples: an online community sample of 480 participants, and a clinical sample of 147 inpatients admitted to a psychiatric hospital after a suicidal attempt or severe suicidal crisis. Confirmatory Factor analysis (CFA) was used to test whether the proposed structure fits the data. In both samples, bootstrapped exploratory graph analysis suggested that the defeat and entrapment items belonged to different dimensions. Within the entrapment items, two separate dimensions were detected, labelled internal and external entrapment. Defeat appeared to be multifaceted only in the online sample. When comparing the CFA outcomes of the one, two, three and four factor models, the one factor model was preferred. Defeat and entrapment can be viewed as distinct, yet, highly associated constructs. Thus, although replication is needed, results are in line with theories differentiating between these two constructs.

Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving

Science.gov (United States)

González-Miranda, J. M.

1998-06-01

Chaotic systems, when used to drive copies of themselves (or parts of themselves) may induce interesting behaviors in the driven system. In case the later exhibits invariance under amplification or translation, they may show amplification (reduction), or displacement of the attractor. It is shown how the behavior to be obtained is implied by the symmetries involved. Two explicit examples are studied to show how these phenomena manifest themselves under perfect and imperfect coupling.

Commentary on "A non-reward attractor theory of depression" : A proposal to include the habenula connection

NARCIS (Netherlands)

Loonen, Anton J M; Ivanova, Svetlana A

2017-01-01

The non-reward attractor theory of depression describes this mood disorder as originating from a neuronal dysfunction that arises from increased vulnerability of a cortical network that detects failure to receive an expected reward. From an evolutionary standpoint, the concept that the cerebral

Analysis of fractal dimensions of rat bones from film and digital images

Science.gov (United States)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

2001-01-01

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems

Science.gov (United States)

Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Hashemi Golpayegani, S. Mohammad Reza; Almasganj, Farshad

2015-02-01

As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.

Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit

International Nuclear Information System (INIS)

Njitacke, Z.T.; Kengne, J.; Fotsin, H.B.; Negou, A. Nguomkam; Tchiotsop, D.

2016-01-01

In the present paper, a new memristor based oscillator is obtained from the autonomous Jerk circuit [Kengne et al., Nonlinear Dynamics (2016) 83: 751̶765] by substituting the nonlinear element of the original circuit with a first order memristive diode bridge. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. Various nonlinear analysis tools such as phase portraits, time series, bifurcation diagrams, Poincaré section and the spectrum of Lyapunov exponents are exploited to characterize different scenarios to chaos in the novel circuit. It is found that the system experiences period doubling and crisis routes to chaos. One of the major results of this work is the finding of a window in the parameters’ space in which the circuit develops hysteretic behaviors characterized by the coexistence of four different (periodic and chaotic) attractors for the same values of the system parameters. Basins of attractions of various coexisting attractors are plotted showing complex basin boundaries. As far as the authors’ knowledge goes, the novel memristive jerk circuit represents one of the simplest electrical circuits (no analog multiplier chip is involved) capable of four disconnected coexisting attractors reported to date. Both PSpice simulations of the nonlinear dynamics of the oscillator and laboratory experimental measurements are carried out to validate the theoretical analysis.

Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force.

Science.gov (United States)

Senthilkumar, D V; Srinivasan, K; Thamilmaran, K; Lakshmanan, M

2008-12-01

We identify an unconventional route to the creation of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square-wave-type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the creation of the SNA; we term this the bubbling route to the SNA. We characterize and confirm this creation from both experimental and numerical data using maximal Lyapunov exponents and their variance, Poincaré maps, Fourier amplitude spectra, and spectral distribution functions. We also strongly confirm the creation of a SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.

Characterization of the disruption of neural control strategies for dynamic fingertip forces from attractor reconstruction.

Directory of Open Access Journals (Sweden)

Lorenzo Peppoloni

Full Text Available The Strength-Dexterity (SD test measures the ability of the pulps of the thumb and index finger to compress a compliant and slender spring prone to buckling at low forces (<3N. We know that factors such as aging and neurodegenerative conditions bring deteriorating physiological changes (e.g., at the level of motor cortex, cerebellum, and basal ganglia, which lead to an overall loss of dexterous ability. However, little is known about how these changes reflect upon the dynamics of the underlying biological system. The spring-hand system exhibits nonlinear dynamical behavior and here we characterize the dynamical behavior of the phase portraits using attractor reconstruction. Thirty participants performed the SD test: 10 young adults, 10 older adults, and 10 older adults with Parkinson's disease (PD. We used delayed embedding of the applied force to reconstruct its attractor. We characterized the distribution of points of the phase portraits by their density (number of distant points and interquartile range and geometric features (trajectory length and size. We find phase portraits from older adults exhibit more distant points (p = 0.028 than young adults and participants with PD have larger interquartile ranges (p = 0.001, trajectory lengths (p = 0.005, and size (p = 0.003 than their healthy counterparts. The increased size of the phase portraits with healthy aging suggests a change in the dynamical properties of the system, which may represent a weakening of the neural control strategy. In contrast, the distortion of the attractor in PD suggests a fundamental change in the underlying biological system, and disruption of the neural control strategy. This ability to detect differences in the biological mechanisms of dexterity in healthy and pathological aging provides a simple means to assess their disruption in neurodegenerative conditions and justifies further studies to understand the link with the physiological changes.

Tidal volume estimation using the blanket fractal dimension of the tracheal sounds acquired by smartphone.

Science.gov (United States)

Reljin, Natasa; Reyes, Bersain A; Chon, Ki H

2015-04-27

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.

Tidal Volume Estimation Using the Blanket Fractal Dimension of the Tracheal Sounds Acquired by Smartphone

Directory of Open Access Journals (Sweden)

Natasa Reljin

2015-04-01

Full Text Available In this paper, we propose the use of blanket fractal dimension (BFD to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5 healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE. The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained. The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.

Self-organizing path integration using a linked continuous attractor and competitive network: path integration of head direction.

Science.gov (United States)

Stringer, Simon M; Rolls, Edmund T

2006-12-01

A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.

Oscillatory attractors: a new cosmological phase

Energy Technology Data Exchange (ETDEWEB)

Bains, Jasdeep S. [Center for the Fundamental Laws of Nature, Harvard University, 17 Oxford St, Cambridge, MA 02138 (United States); Hertzberg, Mark P. [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, 574 Boston Ave, Medford, MA 02155 (United States); Wilczek, Frank, E-mail: bains@physics.harvard.edu, E-mail: mark.hertzberg@tufts.edu, E-mail: wilczek@mit.edu [Center for Theoretical Physics, Department of Physics, MIT, 77 Massachusetts Ave, Cambridge, MA 02139 (United States)

2017-05-01

In expanding FRW spacetimes, it is usually the case that homogeneous scalar fields redshift and their amplitudes approach limiting values: Hubble friction usually ensures that the field relaxes to its minimum energy configuration, which is usually a static configuration. Here we discover a class of relativistic scalar field models in which the attractor behavior is the field oscillating indefinitely, with finite amplitude, in an expanding FRW spacetime, despite the presence of Hubble friction. This is an example of spontaneous breaking of time translation symmetry. We find that the effective equation of state of the field has average value ( w )=−1, implying that the field itself could drive an inflationary or dark energy dominated phase. This behavior is reminiscent of ghost condensate models, but in the new models, unlike in the ghost condensate models, the energy-momentum tensor is time dependent, so that these new models embody a more definitive breaking of time translation symmetry. We explore (quantum) fluctuations around the homogeneous background solution, and find that low k -modes can be stable, while high k -modes are typically unstable. We discuss possible interpretations and implications of that instability.

Estimating seabed pressure from demersal trawls, seines, and dredges based on gear design and dimensions

DEFF Research Database (Denmark)

Eigaard, Ole Ritzau; Bastardie, Francois; Breen, Mike

2016-01-01

such as logbook data. Here, we take a different approach starting from the gear itself (design and dimensions) to estimate the physical interactions with the seabed at the level of the individual fishing operation. We defined 14 distinct towed gear groups in European waters (eight otter trawl groups, three beam...... trawl groups, two demersal seine groups, and one dredge group), for which we established gear “footprints”. The footprint of a gear is defined as the relative contribution from individual larger gear components, such as trawl doors, sweeps, and groundgear, to the total area and severity of the gear...... to enable the prediction of gear footprint area and sediment penetration from vessel size. Application of these relationships with average vessel sizes and towing speeds provided hourly swept-area estimates by métier. Scottish seining has the largest overall gear footprint of ∼1.6 km2 h−1 of which 0.08 km2...

Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

Science.gov (United States)

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

On the global attractor of 2D incompressible turbulence with random forcing

Science.gov (United States)

Emami, Pedram; Bowman, John C.

2018-03-01

This study revisits bounds on the projection of the global attractor in the energy-enstrophy plane for 2D incompressible turbulence [Dascaliuc, Foias, and Jolly, 2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in particular often use a stochastic white-noise forcing to achieve a prescribed mean energy injection rate. The analytical bounds are demonstrated numerically for the case of white-noise forcing.

Discrete simulations of spatio-temporal dynamics of small water bodies under varied stream flow discharges

Science.gov (United States)

Daya Sagar, B. S.

2005-01-01

Spatio-temporal patterns of small water bodies (SWBs) under the influence of temporally varied stream flow discharge are simulated in discrete space by employing geomorphologically realistic expansion and contraction transformations. Cascades of expansion-contraction are systematically performed by synchronizing them with stream flow discharge simulated via the logistic map. Templates with definite characteristic information are defined from stream flow discharge pattern as the basis to model the spatio-temporal organization of randomly situated surface water bodies of various sizes and shapes. These spatio-temporal patterns under varied parameters (λs) controlling stream flow discharge patterns are characterized by estimating their fractal dimensions. At various λs, nonlinear control parameters, we show the union of boundaries of water bodies that traverse the water body and non-water body spaces as geomorphic attractors. The computed fractal dimensions of these attractors are 1.58, 1.53, 1.78, 1.76, 1.84, and 1.90, respectively, at λs of 1, 2, 3, 3.46, 3.57, and 3.99. These values are in line with general visual observations.

Discrete simulations of spatio-temporal dynamics of small water bodies under varied stream flow discharges

Directory of Open Access Journals (Sweden)

B. S. Daya Sagar

2005-01-01

Full Text Available Spatio-temporal patterns of small water bodies (SWBs under the influence of temporally varied stream flow discharge are simulated in discrete space by employing geomorphologically realistic expansion and contraction transformations. Cascades of expansion-contraction are systematically performed by synchronizing them with stream flow discharge simulated via the logistic map. Templates with definite characteristic information are defined from stream flow discharge pattern as the basis to model the spatio-temporal organization of randomly situated surface water bodies of various sizes and shapes. These spatio-temporal patterns under varied parameters (λs controlling stream flow discharge patterns are characterized by estimating their fractal dimensions. At various λs, nonlinear control parameters, we show the union of boundaries of water bodies that traverse the water body and non-water body spaces as geomorphic attractors. The computed fractal dimensions of these attractors are 1.58, 1.53, 1.78, 1.76, 1.84, and 1.90, respectively, at λs of 1, 2, 3, 3.46, 3.57, and 3.99. These values are in line with general visual observations.

Explosive attractor solutions to a universal cubic delay equation

Science.gov (United States)

Sanz-Orozco, D.; Berk, H. L.

2017-05-01

New explosive attractor solutions have been found in a universal cubic delay equation that has been studied in both the plasma and the fluid mechanics literature. Through computational simulations and analytic approximations, it is found that the oscillatory component of the explosive mode amplitude solutions are described through multi-frequency Fourier expansions with respect to a pseudo-time variable. The spectral dependence of these solutions as a function of a system parameter, ϕ , is studied. The mode amplitude that is described in the explosive regime has two main features: a well-known envelope ( t 0 - t ) - 5 / 2 , with t0 the blow-up time of the amplitude, and a spectrum of discrete oscillations with ever-increasing frequencies, which may give experimental information about the properties of a system's equilibrium.

Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems

Science.gov (United States)

Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya

2017-02-01

Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing the rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of the system state, i.e., deviations from the limit-cycle attractor, has been introduced to describe the transient dynamics around the limit cycle [Wilson and Moehlis, Phys. Rev. E 94, 052213 (2016)]. In this study, we introduce a framework for a reduced phase-amplitude description of transient dynamics of stable limit-cycling systems. In contrast to the preceding study, the isostables are treated in a fully consistent way with the Koopman operator analysis, which enables us to avoid discontinuities of the isostables and to apply the framework to system states far from the limit cycle. We also propose a new, convenient bi-orthogonalization method to obtain the response functions of the amplitudes, which can be interpreted as an extension of the adjoint covariant Lyapunov vector to transient dynamics in limit-cycling systems. We illustrate the utility of the proposed reduction framework by estimating the optimal injection timing of external input that efficiently suppresses deviations of the system state from the limit cycle in a model of a biochemical oscillator.

Relationship Between Adult Renal Dimensions and Biometric ...

African Journals Online (AJOL)

We measured renal dimensions sonographically and correlated the values obtained with some anthropometric parameters in order to identify the best estimate of renal size in a clinical setting. The renal dimensions of 200 adult subjects referred for abdomino-pelvic scan at University of Nigeria Teaching Hospital, Enugu ...

Cosmological attractors and anisotropies in two measure theories, effective EYMH systems, and off-diagonal inflation models

Energy Technology Data Exchange (ETDEWEB)

Rajpoot, Subhash [California State University, Long Beach, CA (United States); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' , Project IDEI, Iasi (Romania)

2017-05-15

Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein-Yang-Mills-Higgs, and two measure theories. The types of models considered are Freedman-Lemaitre-Robertson-Walker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateau-type inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented. (orig.)

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability.

Science.gov (United States)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-01-01

By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived in this paper. The system state equations are composed of nine terms including only one constant term. Depending on the different values of the constant term, this new proposed system has a line of equilibrium points or no equilibrium points. Compared with other similar chaotic systems, the newly presented system owns more abundant and complicated dynamic properties. What interests us is the observation that if the value of the constant term of the system is nonzero, it has no equilibria, and therefore, the Shil'nikov theorem is not suitable to verify the existence of chaos for the lack of heteroclinic or homoclinic trajectory. However, one-wing, two-wing, three-wing, and four-wing hidden attractors can be obtained from this new system. In addition, various coexisting hidden attractors are obtained and the complex transient transition behaviors are also observed. More interestingly, the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises. The rich and complex hidden dynamic characteristics of this system are investigated by phase portraits, bifurcation diagrams, Lyapunov exponents, and so on. Finally, the new system is implemented by an electronic circuit. A very good agreement is observed between the experimental results and the numerical simulations of the same system on the Matlab platform.

Low-dimensional chaos in a hydrodynamic system

International Nuclear Information System (INIS)

Brandstater, A.; Swift, J.; Swinney, H.L.; Wolf, A.; Farmer, J.D.; Jen, E.; Crutchfield, J.P.

1983-01-01

Evidence is presented for low-dimensional strange attractors in Couette-Taylor flow data. Computations of the largest Lyapunov exponent and metric entropy show that the system displays sensitive dependence on initial conditions. Although the phase space is very high dimensional, analysis of experimental data shows that motion is restricted to an attractor of dimension less than 5 for Reynolds numbers up to 30% above the onset of chaos. The Lyapunov exponent, entropy, and dimension all generally increase with Reynolds number

Estimate of the angular dimensions of objects and reconstruction of their shapes from the parameters of the fourth-order radiation correlation function

International Nuclear Information System (INIS)

Buryi, E V; Kosygin, A A

2004-01-01

It is shown that, when the angular resolution of a receiving optical system is insufficient, the angular dimensions of a located object can be estimated and its shape can be reconstructed by estimating the parameters of the fourth-order correlation function (CF) of scattered coherent radiation. The reliability of the estimates of CF counts obtained by the method of a discrete spatial convolution of the intensity-field counts, the possibility of estimating the CF profile counts by the method of one-dimensional convolution of intensity counts, and the applicability of the method for reconstructing the object shape are confirmed experimentally. (laser applications and other topics in quantum electronics)

Estimation of seafloor impact from demersal trawls, seines and dredges based on gear design and dimensions

DEFF Research Database (Denmark)

Eigaard, Ole Ritzau; Bastardie, Francois; Breen, Michael

a different approach using the gear itself (design and dimensions) for understanding and estimation of the physical interactions with the seafloor at the individual fishing operation level. With reference to the métier groupings of EU logbooks, we defined 17 distinct towed gear groups in European waters (11...... otter trawl groups, 3 beam trawl groups, 2 demersal seine groups, and 1 dredge group), for which we established seafloor “footprints”. The footprint of a gear was defined as the relative contribution from individual larger gear components, such as the trawl doors, sweeps and ground gear, to the total...... types based on a review of the scientific literature. For each defined gear group a vessel-size (kW or total length) – gear size (total gear width or circumference) relationship was estimated to enable the prediction of gear footprint area and sediment penetration from vessel size. The implications...

The identification of model effective dimensions using global sensitivity analysis

International Nuclear Information System (INIS)

Kucherenko, Sergei; Feil, Balazs; Shah, Nilay; Mauntz, Wolfgang

2011-01-01

It is shown that the effective dimensions can be estimated at reasonable computational costs using variance based global sensitivity analysis. Namely, the effective dimension in the truncation sense can be found by using the Sobol' sensitivity indices for subsets of variables. The effective dimension in the superposition sense can be estimated by using the first order effects and the total Sobol' sensitivity indices. The classification of some important classes of integrable functions based on their effective dimension is proposed. It is shown that it can be used for the prediction of the QMC efficiency. Results of numerical tests verify the prediction of the developed techniques.

The identification of model effective dimensions using global sensitivity analysis

Energy Technology Data Exchange (ETDEWEB)

Kucherenko, Sergei, E-mail: s.kucherenko@ic.ac.u [CPSE, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Feil, Balazs [Department of Process Engineering, University of Pannonia, Veszprem (Hungary); Shah, Nilay [CPSE, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Mauntz, Wolfgang [Lehrstuhl fuer Anlagensteuerungstechnik, Fachbereich Chemietechnik, Universitaet Dortmund (Germany)

2011-04-15

It is shown that the effective dimensions can be estimated at reasonable computational costs using variance based global sensitivity analysis. Namely, the effective dimension in the truncation sense can be found by using the Sobol' sensitivity indices for subsets of variables. The effective dimension in the superposition sense can be estimated by using the first order effects and the total Sobol' sensitivity indices. The classification of some important classes of integrable functions based on their effective dimension is proposed. It is shown that it can be used for the prediction of the QMC efficiency. Results of numerical tests verify the prediction of the developed techniques.

Induced gravity and the attractor dynamics of dark energy/dark matter

International Nuclear Information System (INIS)

Cervantes-Cota, Jorge L.; Putter, Roland de; Linder, Eric V.

2010-01-01

Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity enlarges the dynamical behavior; we consider both couplings together, which can ameliorate some problems for each individually. Such theories have also been proposed in a Higgs-like fashion to induce gravity and unify dark energy and dark matter origins. We explore restrictions on such theories due to their dynamical behavior compared to observations of the cosmic expansion. Quartic potentials in particular have viable stability properties and asymptotically approach general relativity

Detection of strong attractors in social media networks.

Science.gov (United States)

Qasem, Ziyaad; Jansen, Marc; Hecking, Tobias; Hoppe, H Ulrich

2016-01-01

Detection of influential actors in social media such as Twitter or Facebook plays an important role for improving the quality and efficiency of work and services in many fields such as education and marketing. The work described here aims to introduce a new approach that characterizes the influence of actors by the strength of attracting new active members into a networked community. We present a model of influence of an actor that is based on the attractiveness of the actor in terms of the number of other new actors with which he or she has established relations over time. We have used this concept and measure of influence to determine optimal seeds in a simulation of influence maximization using two empirically collected social networks for the underlying graphs. Our empirical results on the datasets demonstrate that our measure stands out as a useful measure to define the attractors comparing to the other influence measures.

Octodon Degus: A Strong Attractor for Alzheimer Research

Directory of Open Access Journals (Sweden)

Rafael Castro-Fuentes

2013-01-01

Full Text Available   The most popular animal models of Alzheimer’s disease (AD are transgenic mice expressing human genes with known mutations which do not represent the most abundant sporadic form of the disease. An increasing number of genetic, vascular and psychosocial data strongly support that the Octodon degus, a moderate-sized and diurnal precocial rodent, provides a naturalistic model for the study of the early neurodegenerative process associated with sporadic AD. In this minireview we describe and analyze the risk factors that contribute to Alzheimer-like characteristics in the degus, following recent publications, and establish some guidelines for future studies in this model of natural aging associated with the disease. Given the heterogeneity of current data derived from the diverse transgenic animal models of AD, now may be the time for the degus to become a strong attractor for academic research labs and companies involved with AD. This may help to understand the mechanisms responsible for the early neurodegenerative process associated with this devastating disease.

Octodon Degus: A Strong Attractor for Alzheimer Research

Directory of Open Access Journals (Sweden)

Rafael Castro-Fuentes

2013-02-01

Full Text Available The most popular animal models of Alzheimer’s disease (AD are transgenic mice expressing human genes with known mutations which do not represent the most abundant sporadic form of the disease. An increasing number of genetic, vascular and psychosocial data strongly support that the Octodon degus, a moderate-sized and diurnal precocial rodent, provides a naturalistic model for the study of the early neurodegenerative process associated with sporadic AD. In this minireview we describe and analyze the risk factors that contribute to Alzheimer-like characteristics in the degus, following recent publications, and establish some guidelines for future studies in this model of natural aging associated with the disease. Given the heterogeneity of current data derived from the diverse transgenic animal models of AD, now may be the time for the degus to become a strong attractor for academic research labs and companies involved with AD. This may help to understand the mechanisms responsible for the early neurodegenerative process associated with this devastating disease.

Noether symmetry approach in the cosmological alpha-attractors

Science.gov (United States)

Kaewkhao, Narakorn; Kanesom, Thanyagamon; Channuie, Phongpichit

2018-06-01

In cosmological framework, Noether symmetry technique has revealed a useful tool in order to examine exact solutions. In this work, we first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the Lagrangian equivalent to Einstein-frame form. We then analyze the dynamics of the field in the cosmological alpha-attractors using the Noether symmetry approach by focusing on the single field scenario in the Einstein-frame form. We show that with a Noether symmetry the corresponding dynamical system can be completely integrated and the potential exhibited by the symmetry can be exactly obtained. With the proper choice of parameters, the behavior of the scale factor displays an exponential (de Sitter) behavior at the present epoch. Moreover, we discover that the Hubble parameters strongly depends on the initial values of parameters exhibited by the Noether symmetry. Interestingly, it can retardedly evolve and becomes a constant in the present epoch in all cases.

Correlation dimension and phase space contraction via extreme value theory

Science.gov (United States)

Faranda, Davide; Vaienti, Sandro

2018-04-01

We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.

LDR: A Package for Likelihood-Based Sufficient Dimension Reduction

Directory of Open Access Journals (Sweden)

R. Dennis Cook

2011-03-01

Full Text Available We introduce a new mlab software package that implements several recently proposed likelihood-based methods for sufficient dimension reduction. Current capabilities include estimation of reduced subspaces with a fixed dimension d, as well as estimation of d by use of likelihood-ratio testing, permutation testing and information criteria. The methods are suitable for preprocessing data for both regression and classification. Implementations of related estimators are also available. Although the software is more oriented to command-line operation, a graphical user interface is also provided for prototype computations.

Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

Science.gov (United States)

Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

2013-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

New measurements of distances to spirals in the great attractor - Further confirmation of the large-scale flow

International Nuclear Information System (INIS)

Dressler, A.; Faber, S.M.

1990-01-01

H-alpha rotation curves and CCD photometry have been obtained for 117 Sb-Sc spiral galaxies in the direction of the large-scale streaming flow. By means of the Tully-Fisher relation, these data are used to predict distances to these galaxies and, by comparison with their observed radial velocities, their peculiar motions relative to a smooth Hubble flow. The new data confirm the results of the earlier studies of a coherent flow pattern in a large region called the 'great attractor'. For the first time, evidence is found for backside infall into the great attractor. Taken as a whole, the data sets for E, S0, and spiral galaxies support the model proposed by Lynden-Bell et al. (1988) of a large, extended overdensity centered at about 45/h Mpc that perturbs the Hubble flow over a region less than about 100/h Mpc in diameter. Observation of the full 's-wave' in the Hubble flow establishes this scale for the structure, providing a strong constraint for models of structure formation, like those based on hot or cold dark matter. 24 refs

Spectral dimension in causal set quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Mizera, Sebastian

2014-01-01

We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can be connected to the nonlocality of causal set theory that is deeply rooted in its fundamentally Lorentzian nature. Based on its large-scale behaviour, we conjecture that the spectral dimension can serve as a tool to distinguish causal sets that approximate manifolds from those that do not. As a new tool to probe quantum spacetime in different quantum gravity approaches, we introduce a novel dimensional estimator, the causal spectral dimension, based on the meeting probability of two random walkers, which respect the causal structure of the quantum spacetime. We discuss a causal-set example, where the spectral dimension and the causal spectral dimension differ, due to the existence of a preferred foliation. (paper)

Conformal dimension theory and application

CERN Document Server

Mackay, John M

2010-01-01

Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed ...

Seven-Disk Manifold, alpha-attractors and B-modes

CERN Document Server

Ferrara, Sergio

2016-01-01

Cosmological alpha-attractor models in \\cN=1 supergravity are based on hyperbolic geometry of a Poincar\\'e disk with the radius square {\\cal R}^2=3\\alpha. The predictions for the B-modes, r\\approx 3\\alpha {4\\over N^2}, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M-theory compactified on a 7-manifold with G_2 holonomy, with a special choice of Betti numbers, one can obtain d=4 \\cN=1 supergravity with rank 7 scalar coset \\Big[{SL(2)\\over SO(2)}\\Big]^7. In a model where these 7 unit size Poincar\\'e disks have identified moduli one finds that 3 alpha =7. Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M-theory, one would predict r \\approx 10^{-2} for 53 e-foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 alpha =1,2,3,4,5,6,7.

Period-doubling cascades and strange attractors in the triple-well Φ6-Van der Pol oscillator

International Nuclear Information System (INIS)

Yu Jun; Zhang Rongbo; Pan Weizhen; Schimansky-Geier, L

2008-01-01

Duffing-Van der Pol equation with the fifth nonlinear-restoring force is investigated. The bifurcation structure and chaotic motion under the periodic perturbation are obtained by numerical simulations. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, phase portraits and Poincare maps, exhibit some new complex dynamical behaviors of the system. Different routes to chaos, such as period doubling and quasi-periodic routes, and various kinds of strange attractors are also demonstrated

The attractor recurrent neural network based on fuzzy functions: An effective model for the classification of lung abnormalities.

Science.gov (United States)

Khodabakhshi, Mohammad Bagher; Moradi, Mohammad Hassan

2017-05-01

The respiratory system dynamic is of high significance when it comes to the detection of lung abnormalities, which highlights the importance of presenting a reliable model for it. In this paper, we introduce a novel dynamic modelling method for the characterization of the lung sounds (LS), based on the attractor recurrent neural network (ARNN). The ARNN structure allows the development of an effective LS model. Additionally, it has the capability to reproduce the distinctive features of the lung sounds using its formed attractors. Furthermore, a novel ARNN topology based on fuzzy functions (FFs-ARNN) is developed. Given the utility of the recurrent quantification analysis (RQA) as a tool to assess the nature of complex systems, it was used to evaluate the performance of both the ARNN and the FFs-ARNN models. The experimental results demonstrate the effectiveness of the proposed approaches for multichannel LS analysis. In particular, a classification accuracy of 91% was achieved using FFs-ARNN with sequences of RQA features. Copyright © 2017 Elsevier Ltd. All rights reserved.

Models for leaf area estimation in dwarf pigeon pea by leaf dimensions

Directory of Open Access Journals (Sweden)

Rafael Vieira Pezzini

2018-03-01

Full Text Available ABSTRACT This study aims to determine the most suitable model to estimate the leaf area of dwarf pigeon pea in function of the leaf central leaflet dimension. Six samplings of 200 leaves were performed in the first experiment, at 36, 42, 50, 56, 64, and 72 days after emergence (DAE. In the second experiment, seven samplings of 200 leaves were performed at 29, 36, 43, 49, 57, 65, and 70 DAE, totaling 2600 leaves. The length (L and width (W of the central leaflet were measured in all leaves composed by left, central, and right leaflets, the product of length times width (LW was calculated, and the leaf area (Y – sum of left, central, and right leaflet areas was determined by digital images. Linear, power, quadratic, and cubic models of Y as function of L, W, and LW were built using data from the second experiment. Leaves from the first experiment were used to validate the models. In dwarf pigeon pea, the linear (Ŷ = – 0.4088 + 1.6669x, R2 = 0.9790 is preferable, but power (Ŷ = 1.6097x1.0065, R2 = 0.9766, quadratic (Ŷ = – 0.3625 + 1.663x + 0.00007x2, R2 = 0.9790, and cubic (Ŷ = 0.7216 + 1.522x + 0.005x2 – 5E–05x3, R2 = 0.9791 models in function of LW are also suitable to estimate the leaf area obtained by digital images. The power model (Ŷ = 5.2508x1.7868, R2 = 0.95 based on the central leaflet width is less laborious because requires only one variable, but it presents accuracy reduction.

SNP-based heritability estimates of the personality dimensions and polygenic prediction of both neuroticism and major depression: findings from CONVERGE.

Science.gov (United States)

Docherty, A R; Moscati, A; Peterson, R; Edwards, A C; Adkins, D E; Bacanu, S A; Bigdeli, T B; Webb, B T; Flint, J; Kendler, K S

2016-10-25

Biometrical genetic studies suggest that the personality dimensions, including neuroticism, are moderately heritable (~0.4 to 0.6). Quantitative analyses that aggregate the effects of many common variants have recently further informed genetic research on European samples. However, there has been limited research to date on non-European populations. This study examined the personality dimensions in a large sample of Han Chinese descent (N=10 064) from the China, Oxford, and VCU Experimental Research on Genetic Epidemiology study, aimed at identifying genetic risk factors for recurrent major depression among a rigorously ascertained cohort. Heritability of neuroticism as measured by the Eysenck Personality Questionnaire (EPQ) was estimated to be low but statistically significant at 10% (s.e.=0.03, P=0.0001). In addition to EPQ, neuroticism based on a three-factor model, data for the Big Five (BF) personality dimensions (neuroticism, openness, conscientiousness, extraversion and agreeableness) measured by the Big Five Inventory were available for controls (n=5596). Heritability estimates of the BF were not statistically significant despite high power (>0.85) to detect heritabilities of 0.10. Polygenic risk scores constructed by best linear unbiased prediction weights applied to split-half samples failed to significantly predict any of the personality traits, but polygenic risk for neuroticism, calculated with LDpred and based on predictive variants previously identified from European populations (N=171 911), significantly predicted major depressive disorder case-control status (P=0.0004) after false discovery rate correction. The scores also significantly predicted EPQ neuroticism (P=6.3 × 10 -6 ). Factor analytic results of the measures indicated that any differences in heritabilities across samples may be due to genetic variation or variation in haplotype structure between samples, rather than measurement non-invariance. Findings demonstrate that neuroticism

Parsing in a Dynamical System: An Attractor-Based Account of the Interaction of Lexical and Structural Constraints in Sentence Processing.

Science.gov (United States)

Tabor, Whitney; And Others

1997-01-01

Proposes a dynamical systems approach to parsing in which syntactic hypotheses are associated with attractors in a metric space. The experiments discussed documented various contingent frequency effects that cut across traditional linguistic grains, each of which was predicted by the dynamical systems model. (47 references) (Author/CK)

Invariant polygons in systems with grazing-sliding.

Science.gov (United States)

Szalai, R; Osinga, H M

2008-06-01

The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.

Hebbian plasticity realigns grid cell activity with external sensory cues in continuous attractor models

Directory of Open Access Journals (Sweden)

Marcello eMulas

2016-02-01

Full Text Available After the discovery of grid cells, which are an essential component to understand how the mammalian brain encodes spatial information, three main classes of computational models were proposed in order to explain their working principles. Amongst them, the one based on continuous attractor networks (CAN, is promising in terms of biological plausibility and suitable for robotic applications. However, in its current formulation, it is unable to reproduce important electrophysiological findings and cannot be used to perform path integration for long periods of time. In fact, in absence of an appropriate resetting mechanism, the accumulation of errors overtime due to the noise intrinsic in velocity estimation and neural computation prevents CAN models to reproduce stable spatial grid patterns. In this paper, we propose an extension of the CAN model using Hebbian plasticity to anchor grid cell activity to environmental landmarks. To validate our approach we used as input to the neural simulations both artificial data and real data recorded from a robotic setup. The additional neural mechanism can not only anchor grid patterns to external sensory cues but also recall grid patterns generated in previously explored environments. These results might be instrumental for next generation bio-inspired robotic navigation algorithms that take advantage of neural computation in order to cope with complex and dynamic environments.

Framework of collagen type I - vasoactive vessels structuring invariant geometric attractor in cancer tissues: insight into biological magnetic field.

Directory of Open Access Journals (Sweden)

Jairo A Díaz

Full Text Available In a previous research, we have described and documented self-assembly of geometric triangular chiral hexagon crystal-like complex organizations (GTCHC in human pathological tissues. This article documents and gathers insights into the magnetic field in cancer tissues and also how it generates an invariant functional geometric attractor constituted for collider partners in their entangled environment. The need to identify this hierarquic attractor was born out of the concern to understand how the vascular net of these complexes are organized, and to determine if the spiral vascular subpatterns observed adjacent to GTCHC complexes and their assembly are interrelational. The study focuses on cancer tissues and all the macroscopic and microscopic material in which GTCHC complexes are identified, which have been overlooked so far, and are rigorously revised. This revision follows the same parameters that were established in the initial phase of the investigation, but with a new item: the visualization and documentation of external dorsal serous vascular bed areas in spatial correlation with the localization of GTCHC complexes inside the tumors. Following the standard of the electro-optical collision model, we were able to reproduce and replicate collider patterns, that is, pairs of left and right hand spin-spiraled subpatterns, associated with the orientation of the spinning process that can be an expansion or contraction disposition of light particles. Agreement between this model and tumor data is surprisingly close; electromagnetic spiral patterns generated were identical at the spiral vascular arrangement in connection with GTCHC complexes in malignant tumors. These findings suggest that the framework of collagen type 1 - vasoactive vessels that structure geometric attractors in cancer tissues with invariant morphology sets generate collider partners in their magnetic domain with opposite biological behavior. If these principles are incorporated

Newton's law in braneworlds with an infinite extra dimension

OpenAIRE

Ito, Masato

2001-01-01

We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.

Fractal dimension of turbulent black holes

Science.gov (United States)

Westernacher-Schneider, John Ryan

2017-11-01

We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

CMB constraints on the inflaton couplings and reheating temperature in α-attractor inflation

Science.gov (United States)

Drewes, Marco; Kang, Jin U.; Mun, Ui Ri

2017-11-01

We study reheating in α-attractor models of inflation in which the inflaton couples to other scalars or fermions. We show that the parameter space contains viable regions in which the inflaton couplings to radiation can be determined from the properties of CMB temperature fluctuations, in particular the spectral index. This may be the only way to measure these fundamental microphysical parameters, which shaped the universe by setting the initial temperature of the hot big bang and contain important information about the embedding of a given model of inflation into a more fundamental theory of physics. The method can be applied to other models of single field inflation.

Sparse Adaptive Channel Estimation Based on lp-Norm-Penalized Affine Projection Algorithm

Directory of Open Access Journals (Sweden)

Yingsong Li

2014-01-01

Full Text Available We propose an lp-norm-penalized affine projection algorithm (LP-APA for broadband multipath adaptive channel estimations. The proposed LP-APA is realized by incorporating an lp-norm into the cost function of the conventional affine projection algorithm (APA to exploit the sparsity property of the broadband wireless multipath channel, by which the convergence speed and steady-state performance of the APA are significantly improved. The implementation of the LP-APA is equivalent to adding a zero attractor to its iterations. The simulation results, which are obtained from a sparse channel estimation, demonstrate that the proposed LP-APA can efficiently improve channel estimation performance in terms of both the convergence speed and steady-state performance when the channel is exactly sparse.

Neuromorphic Implementation of Attractor Dynamics in a Two-Variable Winner-Take-All Circuit with NMDARs: A Simulation Study.

Science.gov (United States)

You, Hongzhi; Wang, Da-Hui

2017-01-01

Neural networks configured with winner-take-all (WTA) competition and N-methyl-D-aspartate receptor (NMDAR)-mediated synaptic dynamics are endowed with various dynamic characteristics of attractors underlying many cognitive functions. This paper presents a novel method for neuromorphic implementation of a two-variable WTA circuit with NMDARs aimed at implementing decision-making, working memory and hysteresis in visual perceptions. The method proposed is a dynamical system approach of circuit synthesis based on a biophysically plausible WTA model. Notably, slow and non-linear temporal dynamics of NMDAR-mediated synapses was generated. Circuit simulations in Cadence reproduced ramping neural activities observed in electrophysiological recordings in experiments of decision-making, the sustained activities observed in the prefrontal cortex during working memory, and classical hysteresis behavior during visual discrimination tasks. Furthermore, theoretical analysis of the dynamical system approach illuminated the underlying mechanisms of decision-making, memory capacity and hysteresis loops. The consistence between the circuit simulations and theoretical analysis demonstrated that the WTA circuit with NMDARs was able to capture the attractor dynamics underlying these cognitive functions. Their physical implementations as elementary modules are promising for assembly into integrated neuromorphic cognitive systems.

Structural alphabets derived from attractors in conformational space

Directory of Open Access Journals (Sweden)

Kleinjung Jens

2010-02-01

Full Text Available Abstract Background The hierarchical and partially redundant nature of protein structures justifies the definition of frequently occurring conformations of short fragments as 'states'. Collections of selected representatives for these states define Structural Alphabets, describing the most typical local conformations within protein structures. These alphabets form a bridge between the string-oriented methods of sequence analysis and the coordinate-oriented methods of protein structure analysis. Results A Structural Alphabet has been derived by clustering all four-residue fragments of a high-resolution subset of the protein data bank and extracting the high-density states as representative conformational states. Each fragment is uniquely defined by a set of three independent angles corresponding to its degrees of freedom, capturing in simple and intuitive terms the properties of the conformational space. The fragments of the Structural Alphabet are equivalent to the conformational attractors and therefore yield a most informative encoding of proteins. Proteins can be reconstructed within the experimental uncertainty in structure determination and ensembles of structures can be encoded with accuracy and robustness. Conclusions The density-based Structural Alphabet provides a novel tool to describe local conformations and it is specifically suitable for application in studies of protein dynamics.

Minimality of invariant laminations for partially hyperbolic attractors

International Nuclear Information System (INIS)

Nobili, Felipe

2015-01-01

Let f : M → M be a C 1 -diffeomorphism over a compact boundaryless Riemannian manifold M, and Λ a compact f-invariant subset of M admitting a partially hyperbolic spliting T f Λ = E s  ⊕ E c  ⊕ E u over the tangent bundle T f Λ. It's known from the Hirsch–Pugh–Shub theory that Λ admits two invariant laminations associated to the extremal bundles E s and E u . These laminations are families of dynamically defined immersed submanifolds of the M tangent, respectively, to the bundles E s and E u at every point in Λ. In this work, we prove that at least one of the invariant laminations of a transitive partially hyperbolic attractor with a one-dimensional center bundle is minimal: the orbit of every leaf intersects Λ densely. This result extends those in Bonatti et al (2002 J. Inst. Math. Jussieu 1 513–41) and Hertz et al (2007 Fields Institute Communications vol 51 (Providence, RI: American Mathematical Society) pp 103–9) about minimal foliations for robustly transitive diffeomorphisms. (paper)

Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

International Nuclear Information System (INIS)

Keefe, L.R.

1984-01-01

The bifurcation structure of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation is investigated analytically and numerically. A rich variety of behavior, including limit cycles, two-tori, period-doubling sequences, and strange attractors are found to exist in the phase space of the solutions constructed from spatial Fourier modes. Beginning with unstable perturbations to the spatially homogeneous Stokes solution, changes in solution behavior are examined as the perturbing wavenumber q is varied in the range 0.6 to 1.3. Solution bifurcations as q changes are often found to be associated with symmetry making or breaking changes in the structure of attractors in phase space. Two distinct mirror image attractors are found to coexist for many values of q. Chaotic motion is found for two ranges of q Lyapunov exponents of the solutions and the Lyapunov dimension of the corresponding attractors are calculated for the larger of these regions. Poincare sections of the attractors within this chaotic range are consistent with the dimension calculation and also reveal a bifurcation structure within the chaos which broadly resembles that found in one-dimensional quadratic maps. The integrability of the Ginzburg-Landau equation is also examined. It is demonstrated that the equation does not possess the Painleve property, except for a special case of the coefficients which corresponds to the integrable non-linear Schroedinger (NLS) equation

Estimation of Stature from Foot Dimensions and Stature among South Indian Medical Students Using Regression Models

Directory of Open Access Journals (Sweden)

Rajesh D. R

2015-01-01

Full Text Available Background: At times fragments of soft tissues are found disposed off in the open, in ditches at the crime scene and the same are brought to forensic experts for the purpose of identification and such type of cases pose a real challenge. Objectives: This study was aimed at developing a methodology which could help in personal identification by studying the relation between foot dimensions and stature among south subjects using regression models. Material and Methods: Stature and foot length of 100 subjects (age range 18-22 years were measured. Linear regression equations for stature estimation were calculated. Result: The correlation coefficients between stature and foot lengths were found to be positive and statistically significant. Height = 98.159 + 3.746 × FLRT (r = 0.821 and Height = 91.242 + 3.284 × FLRT (r = 0.837 are the regression formulas from foot lengths for males and females respectively. Conclusion: The regression equation derived in the study can be used reliably for estimation of stature in a diverse population group thus would be of immense value in the field of personal identification especially from mutilated bodies or fragmentary remains.

The analysis of a novel 3-D autonomous system and circuit implementation

International Nuclear Information System (INIS)

Dong Gaogao; Zheng Song; Tian Lixin; Du Ruijin; Sun Mei; Shi Zhiyan

2009-01-01

This Letter presents a new three-dimensional autonomous system with four quadratic terms. The system with five equilibrium points has complex chaotic dynamics behaviors. It can generate many different single chaotic attractors and double coexisting chaotic attractors over a large range of parameters. We observe that these chaotic attractors were rarely reported in previous work. The complex dynamical behaviors of the system are further investigated by means of phase portraits, Lyapunov exponents spectrum, Lyapunov dimension, dissipativeness of system, bifurcation diagram and Poincare map. The physical circuit experimental results of the chaotic attractors show agreement with numerical simulations. More importantly, the analysis of frequency spectrum shows that the novel system has a broad frequency bandwidth, which is very desirable for engineering applications such as secure communications.

Dimensioning of multiservice links taking account of soft blocking

DEFF Research Database (Denmark)

Iversen, Villy Bæk; Stepanov, S.N.; Kostrov, A.V.

2006-01-01

of a multiservice link taking into account the possibility of soft blocking. An approximate algorithm for estimation of main performance measures is constructed. The error of estimation is numerically studied for different types of soft blocking. The optimal procedure of dimensioning is suggested....

Cancer as quasi-attractor in the gene expression phase space

Science.gov (United States)

Giuliani, A.

2017-09-01

It takes no more than 250 tissue types to build up a metazoan, and each tissue has a specific and largely invariant gene expression signature. This implies the `viable configurations' correspondent to a given activated/inactivated expression pattern over the entire genome are very few. This points to the presence of few `low energy deep valleys' correspondent to the allowed states of the system and is a direct consequence of the fact genes do not work by alone but embedded into genetic expression networks. Statistical thermodynamics formalism focusing on the changes in the degree of correlation of the studied systems allows to detect transition behavior in gene expression phase space resembling the phase transition of physical-chemistry studies. In this realm cancer can be intended as a sort of `parasite' sub-attractor of the corresponding healthy tissue that, in the case of disease, is `kinetically entrapped' into a sub-optimal solution. The consequences of such a state of affair for cancer therapies are potentially huge.

Estimating the dimensions of the SEU-sensitive volume

International Nuclear Information System (INIS)

Abdel-Kader, W.G.; McNulty, P.J.; El-Teleaty, S.; Lynch, J.E.; Khondker, A.N.

1987-01-01

Simulations of the diffusion contribution to charge collection in SEU events are carried out under the simple assumption of random walk. The results of the simulation are combined with calculations of the funneling length for the field-assisted drift components to determine the effective thickness of the sensitive volume element to be used in calculations of soft-error rates for heavy-ion-induced and proton-induced upsets in microelectronic circuits. Comparison is made between predicted and measured SEU cross-sections for devices for which the critical charges are known from electrical measurements and the dimensions of the sensitive volume used are determined by the techniques described. The agreement is sufficient to encourage confidence that SEU rates can be calculated from first principles and a knowledge of the material, structural, and electrical characteristics of the device

Crises-induced intermittencies in a coherently driven system of two-level atoms

International Nuclear Information System (INIS)

Pando L, C.L.; Perez, G.; Cerdeira, H.A.

1993-04-01

We study the coherent dynamics of a thin layer of two-level atoms driven by an external coherent field and a phase conjugated mirror (PCM). Since the variables of the system are defined on the Bloch sphere, the third dimension is provided by the temporal modulation of the Rabi frequencies, which are induced by a PCM which reflects an electric field with a carrier frequency different from the incident one. We show that as the PCM gain coefficient is changed period doubling leading to chaos occurs. We find crises of attractor merging and attractor widening types related to homoclinic and heteroclinic tangencies respectively. For the attractor merging crises we find the critical exponent for the characteristic time of intermittency versus the control parameter which is given by the gain coefficient of the PCM. We show that during the crises of attractor widening type, another crisis due to attractor destruction occurs as the control parameter is changed. The latter is due to the collision of the old attractor with its basin boundary when a new attractor is created. This new attractor is stable only in a very small interval in the neighborhood of this second crisis. (author). 31 refs, 15 figs

Betti multiplets, flows across dimensions and c-extremization

Science.gov (United States)

Amariti, Antonio; Toldo, Chiara

2017-07-01

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0, 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2 d , similarly to the 4d picture, where the exact R-current maximizes the central charge a 4 d . There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

A Quantitative Method for the Analysis of Nomothetic Relationships between Idiographic Structures: Dynamic Patterns Create Attractor States for Sustained Posttreatment Change

Science.gov (United States)

Fisher, Aaron J.; Newman, Michelle G.; Molenaar, Peter C. M.

2011-01-01

Objective: The present article aimed to demonstrate that the establishment of dynamic patterns during the course of psychotherapy can create attractor states for continued adaptive change following the conclusion of treatment. Method: This study is a secondary analysis of T. D. Borkovec and E. Costello (1993). Of the 55 participants in the…

Social media reveal that charismatic species are not the main attractor of ecotourists to sub-Saharan protected areas.

Science.gov (United States)

Hausmann, Anna; Toivonen, Tuuli; Heikinheimo, Vuokko; Tenkanen, Henrikki; Slotow, Rob; Di Minin, Enrico

2017-04-10

Charismatic megafauna are arguably considered the primary attractor of ecotourists to sub-Saharan African protected areas. However, the lack of visitation data across the whole continent has thus far prevented the investigation of whether charismatic species are indeed a key attractor of ecotourists to protected areas. Social media data can now be used for this purpose. We mined data from Instagram, and used generalized linear models with site- and country-level deviations to explore which socio-economic, geographical and biological factors explain social media use in sub-Saharan African protected areas. We found that charismatic species richness did not explain social media usage. On the other hand, protected areas that were more accessible, had sparser vegetation, where human population density was higher, and that were located in wealthier countries, had higher social media use. Interestingly, protected areas with lower richness in non-charismatic species had more users. Overall, our results suggest that more factors than simply charismatic species might explain attractiveness of protected areas, and call for more in-depth content analysis of the posts. With African countries projected to develop further in the near-future, more social media data will become available, and could be used to inform protected area management and marketing.

Diffusion of intrinsic localized modes by attractor hopping

International Nuclear Information System (INIS)

Meister, Matthias; Vazquez, Luis

2003-01-01

Propagating intrinsic localized modes exist in the damped-driven discrete sine-Gordon chain as attractors of the dynamics. The equations of motion of the system are augmented with Gaussian white noise in order to model the effects of temperature on the system. The noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode, which leads to a diffusive motion of the excitation. The Heun method is used to numerically generate the stochastic time-evolution of the configuration. We also present a theoretical model for the diffusion which contains two parameters, a transition probability θ and a delay time τ A . The mean value and the variance of the position of the intrinsic localized mode, obtained from simulations, can be fitted well with the predictions of our model, θ and τ A being used as parameters in the fit. After a transition period following the switching on of the noise, the variance shows a linear behaviour as a function of time and the mean value remains constant. An increase in the strength of the noise lowers the variance, leads to an increase in θ, a decrease in τ A and reduces the average distance a mode travels during the transition period

Diffusion of intrinsic localized modes by attractor hopping

Energy Technology Data Exchange (ETDEWEB)

Meister, Matthias [Dpto FIsica de la Materia Condensada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y FIsica de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza (Spain); Vazquez, Luis [Dpto Matematica Aplicada, Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de AstrobiologIa (CSIC-INTA), 28850 Torrejon de Ardoz (Spain)

2003-11-28

Propagating intrinsic localized modes exist in the damped-driven discrete sine-Gordon chain as attractors of the dynamics. The equations of motion of the system are augmented with Gaussian white noise in order to model the effects of temperature on the system. The noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode, which leads to a diffusive motion of the excitation. The Heun method is used to numerically generate the stochastic time-evolution of the configuration. We also present a theoretical model for the diffusion which contains two parameters, a transition probability {theta} and a delay time {tau}{sub A}. The mean value and the variance of the position of the intrinsic localized mode, obtained from simulations, can be fitted well with the predictions of our model, {theta} and {tau}{sub A} being used as parameters in the fit. After a transition period following the switching on of the noise, the variance shows a linear behaviour as a function of time and the mean value remains constant. An increase in the strength of the noise lowers the variance, leads to an increase in {theta}, a decrease in {tau}{sub A} and reduces the average distance a mode travels during the transition period.

Finite Time Blowup in a Realistic Food-Chain Model

KAUST Repository

Parshad, Rana; Ait Abderrahmane, Hamid; Upadhyay, Ranjit Kumar; Kumari, Nitu

2013-01-01

We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos.

Finite Time Blowup in a Realistic Food-Chain Model

KAUST Repository

Parshad, Rana

2013-05-19

We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos.

Quantifying chaos for ecological stoichiometry.

Science.gov (United States)

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2010-09-01

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Information model of trainee characteristics with definition of stochastic behavior of dynamic system

Science.gov (United States)

Sumin, V. I.; Smolentseva, T. E.; Belokurov, S. V.; Lankin, O. V.

2018-03-01

In the work the process of formation of trainee characteristics with their subsequent change is analyzed and analyzed. Characteristics of trainees were obtained as a result of testing for each section of information on the chosen discipline. The results obtained during testing were input to the dynamic system. The area of control actions consisting of elements of the dynamic system is formed. The limit of deterministic predictability of element trajectories in dynamical systems based on local or global attractors is revealed. The dimension of the phase space of the dynamic system is determined, which allows estimating the parameters of the initial system. On the basis of time series of observations, it is possible to determine the predictability interval of all parameters, which make it possible to determine the behavior of the system discretely in time. Then the measure of predictability will be the sum of Lyapunov’s positive indicators, which are a quantitative measure for all elements of the system. The components for the formation of an algorithm allowing to determine the correlation dimension of the attractor for known initial experimental values of the variables are revealed. The generated algorithm makes it possible to carry out an experimental study of the dynamics of changes in the trainee’s parameters with initial uncertainty.

NON-HAMILTONIAN QUANTUM MECHANICS AND THE NUMERICAL RESEARCHES OF THE ATTRACTOR OF A DYNAMICAL SYSTEM.

Directory of Open Access Journals (Sweden)

A. Weissblut

2012-03-01

Full Text Available This article – introduction to the structural theory of general view dynamical systems, based on construction of dynamic quantum models (DQM, offered by the author. This model is simply connected with traditional model of quantum mechanics (i.e. with the Schrodinger equation. At the same time obtained thus non – Hamiltonian quantum dynamics is easier than classical one: it allow building the clear structural theory and effective algorithms of research for concrete systems. This article is devoted mainly to such task. The algorithm of search for DQM attractors, based on this approach, is offered here.

Generalized correlation integral vectors: A distance concept for chaotic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Haario, Heikki, E-mail: heikki.haario@lut.fi [School of Engineering Science, Lappeenranta University of Technology, Lappeenranta (Finland); Kalachev, Leonid, E-mail: KalachevL@mso.umt.edu [Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812-0864 (United States); Hakkarainen, Janne [Earth Observation Unit, Finnish Meteorological Institute, Helsinki (Finland)

2015-06-15

Several concepts of fractal dimension have been developed to characterise properties of attractors of chaotic dynamical systems. Numerical approximations of them must be calculated by finite samples of simulated trajectories. In principle, the quantities should not depend on the choice of the trajectory, as long as it provides properly distributed samples of the underlying attractor. In practice, however, the trajectories are sensitive with respect to varying initial values, small changes of the model parameters, to the choice of a solver, numeric tolerances, etc. The purpose of this paper is to present a statistically sound approach to quantify this variability. We modify the concept of correlation integral to produce a vector that summarises the variability at all selected scales. The distribution of this stochastic vector can be estimated, and it provides a statistical distance concept between trajectories. Here, we demonstrate the use of the distance for the purpose of estimating model parameters of a chaotic dynamic model. The methodology is illustrated using computational examples for the Lorenz 63 and Lorenz 95 systems, together with a framework for Markov chain Monte Carlo sampling to produce posterior distributions of model parameters.

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

Energy Technology Data Exchange (ETDEWEB)

Elizalde, Emilio; Odintsov, Sergei D. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Campus UAB, Carrer de Can Magrans, s/n, Cerdanyola del Vallès, Barcelona, 08193 Spain (Spain); Pozdeeva, Ekaterina O.; Vernov, Sergey Yu., E-mail: elizalde@ieec.uab.es, E-mail: odintsov@ieec.uab.es, E-mail: pozdeeva@www-hep.sinp.msu.ru, E-mail: svernov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 (Russian Federation)

2016-02-01

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

Unraveling chaotic attractors by complex networks and measurements of stock market complexity

International Nuclear Information System (INIS)

Cao, Hongduo; Li, Ying

2014-01-01

We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel–Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process

Unraveling chaotic attractors by complex networks and measurements of stock market complexity.

Science.gov (United States)

Cao, Hongduo; Li, Ying

2014-03-01

We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.

Speed-Dependent Modulation of the Locomotor Behavior in Adult Mice Reveals Attractor and Transitional Gaits.

Science.gov (United States)

Lemieux, Maxime; Josset, Nicolas; Roussel, Marie; Couraud, Sébastien; Bretzner, Frédéric

2016-01-01

Locomotion results from an interplay between biomechanical constraints of the muscles attached to the skeleton and the neuronal circuits controlling and coordinating muscle activities. Quadrupeds exhibit a wide range of locomotor gaits. Given our advances in the genetic identification of spinal and supraspinal circuits important to locomotion in the mouse, it is now important to get a better understanding of the full repertoire of gaits in the freely walking mouse. To assess this range, young adult C57BL/6J mice were trained to walk and run on a treadmill at different locomotor speeds. Instead of using the classical paradigm defining gaits according to their footfall pattern, we combined the inter-limb coupling and the duty cycle of the stance phase, thus identifying several types of gaits: lateral walk, trot, out-of-phase walk, rotary gallop, transverse gallop, hop, half-bound, and full-bound. Out-of-phase walk, trot, and full-bound were robust and appeared to function as attractor gaits (i.e., a state to which the network flows and stabilizes) at low, intermediate, and high speeds respectively. In contrast, lateral walk, hop, transverse gallop, rotary gallop, and half-bound were more transient and therefore considered transitional gaits (i.e., a labile state of the network from which it flows to the attractor state). Surprisingly, lateral walk was less frequently observed. Using graph analysis, we demonstrated that transitions between gaits were predictable, not random. In summary, the wild-type mouse exhibits a wider repertoire of locomotor gaits than expected. Future locomotor studies should benefit from this paradigm in assessing transgenic mice or wild-type mice with neurotraumatic injury or neurodegenerative disease affecting gait.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

Science.gov (United States)

Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J

2013-06-01

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

Hypothetical neural mechanism that may play a role in mental rotation: an attractor neural network model.

Science.gov (United States)

Benusková, L; Estok, S

1998-11-01

We propose an attractor neural network (ANN) model that performs rotation-invariant pattern recognition in such a way that it can account for a neural mechanism being involved in the image transformation accompanying the experience of mental rotation. We compared the performance of our ANN model with the results of the chronometric psychophysical experiments of Cooper and Shepard (Cooper L A and Shepard R N 1973 Visual Information Processing (New York: Academic) pp 204-7) on discrimination of alphanumeric characters presented in various angular departures from their canonical upright position. Comparing the times required for pattern retrieval in its canonical upright position with the reaction times of human subjects, we found agreement in that (i) retrieval times for clockwise and anticlockwise departures of the same angular magnitude (up to 180 degrees) were not different, (ii) retrieval times increased with departure from upright and (iii) increased more sharply as departure from upright approached 180 degrees. The rotation-invariant retrieval of the activity pattern has been accomplished by means of the modified algorithm of Dotsenko (Dotsenko V S 1988 J. Phys. A: Math. Gen. 21 L783-7) proposed for translation-, rotation- and size-invariant pattern recognition, which uses relaxation of neuronal firing thresholds to guide the evolution of the ANN in state space towards the desired memory attractor. The dynamics of neuronal relaxation has been modified for storage and retrieval of low-activity patterns and the original gradient optimization of threshold dynamics has been replaced with optimization by simulated annealing.

FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY*

Institute of Scientific and Technical Information of China (English)

应阳君; 黄祖洽

2001-01-01

Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

Science.gov (United States)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

Selective Attention to Perceptual Dimensions and Switching between Dimensions

Science.gov (United States)

Meiran, Nachshon; Dimov, Eduard; Ganel, Tzvi

2013-01-01

In the present experiments, the question being addressed was whether switching attention between perceptual dimensions and selective attention to dimensions are processes that compete over a common resource? Attention to perceptual dimensions is usually studied by requiring participants to ignore a never-relevant dimension. Selection failure…

On some dynamical chameleon systems

Science.gov (United States)

Burkin, I. M.; Kuznetsova, O. I.

2018-03-01

It is now well known that dynamical systems can be categorized into systems with self-excited attractors and systems with hidden attractors. A self-excited attractor has a basin of attraction that is associated with an unstable equilibrium, while a hidden attractor has a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. Hidden attractors play the important role in engineering applications because they allow unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing. In addition, complex behaviors of chaotic systems have been applied in various areas from image watermarking, audio encryption scheme, asymmetric color pathological image encryption, chaotic masking communication to random number generator. Recently, researchers have discovered the so-called “chameleon systems”. These systems were so named because they demonstrate self-excited or hidden oscillations depending on the value of parameters. The present paper offers a simple algorithm of synthesizing one-parameter chameleon systems. The authors trace the evolution of Lyapunov exponents and the Kaplan-Yorke dimension of such systems which occur when parameters change.

Algorithms for Brownian first-passage-time estimation

Science.gov (United States)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Irreducible fractal structures for Moran's theorems

Energy Technology Data Exchange (ETDEWEB)

Fernandez-Martinez, M.; Sanchez-Granero, M.A.

2017-07-01

Along this talk, we shall deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of self-similar sets. Clasically, the open set condition has been understood as the right separation condition for IFS-attractors since it becomes a sufficient (though not necessary) condition allowing to easily calculate their similarity dimensions. However, it depends on an external open set. Our contribution consists of a novel separation condition for self-similar sets we shall characterize in terms of the natural fractal structure which any IFS-attractor can be endowed with. We justify that such a separation condition is weaker than the strong open set condition and allows to prove some Moran's type theorems. (Author)

The probability of the creation of extra dimensions in nuclear collisions

International Nuclear Information System (INIS)

Nazarenko, A.V.

2008-01-01

The minisuperspace model in 3+d spatial dimensions with matter described by the bag model is considered with the aim of estimating the probability of creation of compactified extra dimensions in nuclear collisions. The amplitude of transition from three- to (3+d)-dimensional space has been calculated both in the case of completely confined matter, when the contribution of radiation is ignored, and in the case of radiation domination, when the bag constant is negligible. It turns out that the number of additional dimensions is limited in the first regime, while it is infinite in the second one. It is shown that the probability of creation of extra dimensions is finite in both regimes. (author)

Fractal Dimension and Maximum Sunspot Number in Solar Cycle

Directory of Open Access Journals (Sweden)

R.-S. Kim

2006-09-01

Full Text Available The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89 between the observed and predicted maximum sunspot numbers in the solar cycles.

Nonlinear techniques for forecasting solar activity directly from its time series

Science.gov (United States)

Ashrafi, S.; Roszman, L.; Cooley, J.

1993-01-01

This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Characterization of chaotic dynamics in the human menstrual cycle

Science.gov (United States)

Derry, Gregory; Derry, Paula

2010-03-01

The human menstrual cycle exhibits much unexplained variability, which is typically dismissed as random variation. Given the many delayed nonlinear feedbacks in the reproductive endocrine system, however, the menstrual cycle might well be a nonlinear dynamical system in a chaotic trajectory, and that this instead accounts for the observed variability. Here, we test this hypothesis by performing a time series analysis on data for 7438 menstrual cycles from 38 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Using phase space reconstruction techniques with a maximum embedding dimension of 6, we find appropriate scaling behavior in the correlation sums for this data, indicating low dimensional deterministic dynamics. A correlation dimension of 2.6 is measured in this scaling regime, and this result is confirmed by recalculation using the Takens estimator. These results may be interpreted as offering an approximation to the fractal dimension of a strange attractor governing the chaotic dynamics of the menstrual cycle.

Nonlinear Stochastic stability analysis of Wind Turbine Wings by Monte Carlo Simulations

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Iwankiewiczb, R.; Nielsen, Søren R.K.

2007-01-01

and inertial contributions. A reduced two-degrees-of-freedom modal expansion is used specifying the modal coordinate of the fundamental blade and edgewise fixed base eigenmodes of the beam. The rotating beam is subjected to harmonic and narrow-banded support point motion from the nacelle displacement...... under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore......, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations....

Stabilizing embedology: Geometry-preserving delay-coordinate maps

Science.gov (United States)

Eftekhari, Armin; Yap, Han Lun; Wakin, Michael B.; Rozell, Christopher J.

2018-02-01

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

Effective visual working memory capacity: an emergent effect from the neural dynamics in an attractor network.

Directory of Open Access Journals (Sweden)

Laura Dempere-Marco

Full Text Available The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1 the presence of a visually salient item reduces the number of items that can be held in working memory, and 2 visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC in contrast to the maximal upper capacity limit only reached under ideal conditions.

Effective visual working memory capacity: an emergent effect from the neural dynamics in an attractor network.

Science.gov (United States)

Dempere-Marco, Laura; Melcher, David P; Deco, Gustavo

2012-01-01

The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions.

Effective Visual Working Memory Capacity: An Emergent Effect from the Neural Dynamics in an Attractor Network

Science.gov (United States)

Dempere-Marco, Laura; Melcher, David P.; Deco, Gustavo

2012-01-01

The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions. PMID:22952608

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

Science.gov (United States)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

The complexity of computing the MCD-estimator

DEFF Research Database (Denmark)

Bernholt, T.; Fischer, Paul

2004-01-01

In modem statistics the robust estimation of parameters is a central problem, i.e., an estimation that is not or only slightly affected by outliers in the data. The minimum covariance determinant (MCD) estimator (J. Amer. Statist. Assoc. 79 (1984) 871) is probably one of the most important robust...... estimators of location and scatter. The complexity of computing the MCD, however, was unknown and generally thought to be exponential even if the dimensionality of the data is fixed. Here we present a polynomial time algorithm for MCD for fixed dimension of the data. In contrast we show that computing...... the MCD-estimator is NP-hard if the dimension varies. (C) 2004 Elsevier B.V. All rights reserved....

Example of the Smooth Skew Product in the Plane with the One-dimensional Ramified Continuum as the Global Attractor*

Directory of Open Access Journals (Sweden)

Efremova L.S.

2012-08-01

Full Text Available The example is constructed of the C1-smooth skew product of interval maps possessing the one-dimensional ramified continuum (containing no arcs homeomorphic to the circle with an infinite set of ramification points as the global attractor. L’exemple est construit à partir d’un produit biaisé lisse de classe C1 de transformations d’un intervalle, qui a un continuum unidimensionnel ramifié (ne contenant pas d’arcs homéomorphes à un cercle avec un ensemble infini de points de branchement comme attracteur global.

Entropy of the Mixture of Sources and Entropy Dimension

OpenAIRE

Smieja, Marek; Tabor, Jacek

2011-01-01

We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.

The feasibility of remotely sensed data to estimate urban tree dimensions and biomass

Science.gov (United States)

Jun-Hak Lee; Yekang Ko; E. Gregory McPherson

2016-01-01

Accurately measuring the biophysical dimensions of urban trees, such as crown diameter, stem diameter, height, and biomass, is essential for quantifying their collective benefits as an urban forest. However, the cost of directly measuring thousands or millions of individual trees through field surveys can be prohibitive. Supplementing field surveys with remotely sensed...

Emergent properties of gene evolution: Species as attractors in phenotypic space

Science.gov (United States)

Reuveni, Eli; Giuliani, Alessandro

2012-02-01

The question how the observed discrete character of the phenotype emerges from a continuous genetic distance metrics is the core argument of two contrasted evolutionary theories: punctuated equilibrium (stable evolution scattered with saltations in the phenotype) and phyletic gradualism (smooth and linear evolution of the phenotype). Identifying phenotypic saltation on the molecular levels is critical to support the first model of evolution. We have used DNA sequences of ∼1300 genes from 6 isolated populations of the budding yeast Saccharomyces cerevisiae. We demonstrate that while the equivalent measure of the genetic distance show a continuum between lineage distance with no evidence of discrete states, the phenotypic space illustrates only two (discrete) possible states that can be associated with a saltation of the species phenotype. The fact that such saltation spans large fraction of the genome and follows by continuous genetic distance is a proof of the concept that the genotype-phenotype relation is not univocal and may have severe implication when looking for disease related genes and mutations. We used this finding with analogy to attractor-like dynamics and show that punctuated equilibrium could be explained in the framework of non-linear dynamics systems.

Estimating forest ecosystem evapotranspiration at multiple temporal scales with a dimension analysis approach

Science.gov (United States)

Guoyi Zhou; Ge Sun; Xu Wang; Chuanyan Zhou; Steven G. McNulty; James M. Vose; Devendra M. Amatya

2008-01-01

It is critical that evapotranspiration (ET) be quantified accurately so that scientists can evaluate the effects of land management and global change on water availability, streamflow, nutrient and sediment loading, and ecosystem productivity in watersheds. The objective of this study was to derive a new semi-empirical ET modeled using a dimension analysis method that...

Reconstruction of dynamical systems from interspike intervals

International Nuclear Information System (INIS)

Sauer, T.

1994-01-01

Attractor reconstruction from interspike interval (ISI) data is described, in rough analogy with Taken's theorem for attractor reconstruction from time series. Assuming a generic integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence has an important implication: interspike intervals can be forecast from past history. We show that deterministically driven ISI series can be distinguished from stochastically driven ISI series on the basis of prediction error

Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus

Science.gov (United States)

Ito, Takanori; Ito, Kikukatsu

2005-11-01

Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 °C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the “Zazen attractor.” Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.

Fractal dimension analysis in a highly granular calorimeter

CERN Document Server

Ruan, M; Brient, J.C; Jeans, D; Videau, H

2015-01-01

The concept of “particle flow” has been developed to optimise the jet energy resolution by distinguishing the different jet components. A highly granular calorimeter designed for the particle flow algorithm provides an unprecedented level of detail for the reconstruction of calorimeter showers and enables new approaches to shower analysis. In this paper the measurement and use of the fractal dimension of showers is described. The fractal dimension is a characteristic number that measures the global compactness of the shower. It is highly dependent on the primary particle type and energy. Its application in identifying particles and estimating their energy is described in the context of a calorimeter designed for the International Linear Collider.

City Brand Personality—Relations with Dimensions and Dimensions Inter-Relations

Directory of Open Access Journals (Sweden)

Oana Țugulea

2017-12-01

Full Text Available City brand strategies play an important part in building strong identities for cities and also for effective promotional campaigns. The purpose of this research is to analyze in more depth the dimensions of the City Brand Personality of Iași, as identified in previous research. The objectives of the present study are to: (1 understand the impact of each dimension upon the entire construct; (2 identify the possible connections between the perception of the city brand personality and the perceptions on particular city features; (3 identify the possible inter-connections between the resulting dimensions. An Independent Samples t test, Discriminant analysis, and Correlations and Regressions analysis were conducted. The dimension Peacefulness/Sincerity has the highest positive impact, while the dimension Malignacy has the lowest negative impact. Respondents who consider the city to be relatively young rate the personality features better for the dimensions of Peacefulness/Sincerity and Competence. Competence and Peacefulness/Sincerity are strongly related. Improving the perception of features composing the Competence dimension leads to an improvement of the entire City Brand Personality. Future research could specifically identify the types of sustainable activities that could be associated with the desired personality traits.

Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection

Directory of Open Access Journals (Sweden)

Stuart Bartlett

2016-12-01

Full Text Available Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP. However, almost all such investigations were limited to fixed temperature boundary conditions (BCs. It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport. This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of

Adult Education and the Rational-Irrational Dimension of Prejudice

Science.gov (United States)

Rhyne, Dwight C.

1973-01-01

Teachers and counselors in an eight-week institute on problems of school desegregation were used in this study to estimate the degree of change in ethnic attitudes on the rational-irrational and anti-pro minority dimensions of prejudice as related to participation in an intensive adult education experience. (DS)

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

Science.gov (United States)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

Three-dimension reconstruction based on spatial light modulator

International Nuclear Information System (INIS)

Deng Xuejiao; Zhang Nanyang; Zeng Yanan; Yin Shiliang; Wang Weiyu

2011-01-01

Three-dimension reconstruction, known as an important research direction of computer graphics, is widely used in the related field such as industrial design and manufacture, construction, aerospace, biology and so on. Via such technology we can obtain three-dimension digital point cloud from a two-dimension image, and then simulate the three-dimensional structure of the physical object for further study. At present, the obtaining of three-dimension digital point cloud data is mainly based on the adaptive optics system with Shack-Hartmann sensor and phase-shifting digital holography. Referring to surface fitting, there are also many available methods such as iterated discrete fourier transform, convolution and image interpolation, linear phase retrieval. The main problems we came across in three-dimension reconstruction are the extraction of feature points and arithmetic of curve fitting. To solve such problems, we can, first of all, calculate the relevant surface normal vector information of each pixel in the light source coordinate system, then these vectors are to be converted to the coordinates of image through the coordinate conversion, so the expectant 3D point cloud get arise. Secondly, after the following procedures of de-noising, repairing, the feature points can later be selected and fitted to get the fitting function of the surface topography by means of Zernike polynomial, so as to reconstruct the determinand's three-dimensional topography. In this paper, a new kind of three-dimension reconstruction algorithm is proposed, with the assistance of which, the topography can be estimated from its grayscale at different sample points. Moreover, the previous stimulation and the experimental results prove that the new algorithm has a strong capability to fit, especially for large-scale objects .

Three-dimension reconstruction based on spatial light modulator

Science.gov (United States)

Deng, Xuejiao; Zhang, Nanyang; Zeng, Yanan; Yin, Shiliang; Wang, Weiyu

2011-02-01

Three-dimension reconstruction, known as an important research direction of computer graphics, is widely used in the related field such as industrial design and manufacture, construction, aerospace, biology and so on. Via such technology we can obtain three-dimension digital point cloud from a two-dimension image, and then simulate the three-dimensional structure of the physical object for further study. At present, the obtaining of three-dimension digital point cloud data is mainly based on the adaptive optics system with Shack-Hartmann sensor and phase-shifting digital holography. Referring to surface fitting, there are also many available methods such as iterated discrete fourier transform, convolution and image interpolation, linear phase retrieval. The main problems we came across in three-dimension reconstruction are the extraction of feature points and arithmetic of curve fitting. To solve such problems, we can, first of all, calculate the relevant surface normal vector information of each pixel in the light source coordinate system, then these vectors are to be converted to the coordinates of image through the coordinate conversion, so the expectant 3D point cloud get arise. Secondly, after the following procedures of de-noising, repairing, the feature points can later be selected and fitted to get the fitting function of the surface topography by means of Zernike polynomial, so as to reconstruct the determinand's three-dimensional topography. In this paper, a new kind of three-dimension reconstruction algorithm is proposed, with the assistance of which, the topography can be estimated from its grayscale at different sample points. Moreover, the previous stimulation and the experimental results prove that the new algorithm has a strong capability to fit, especially for large-scale objects .

Variable Kernel Density Estimation

OpenAIRE

Terrell, George R.; Scott, David W.

1992-01-01

We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two dimensions, but begin to b...

Chaotic interactions of self-replicating RNA.

Science.gov (United States)

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Estimating volume, biomass, and potential emissions of hand-piled fuels

Science.gov (United States)

Clinton S. Wright; Cameron S. Balog; Jeffrey W. Kelly

2009-01-01

Dimensions, volume, and biomass were measured for 121 hand-constructed piles composed primarily of coniferous (n = 63) and shrub/hardwood (n = 58) material at sites in Washington and California. Equations using pile dimensions, shape, and type allow users to accurately estimate the biomass of hand piles. Equations for estimating true pile volume from simple geometric...

Criteria for the reliability of numerical approximations to the solution of fluid flow problems

International Nuclear Information System (INIS)

Foias, C.

1986-01-01

The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

Forward and adjoint sensitivity computation of chaotic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Qiqi, E-mail: qiqi@mit.edu [Department of Aeronautics and Astronautics, MIT, 77 Mass Ave., Cambridge, MA 02139 (United States)

2013-02-15

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

Geometric k-nearest neighbor estimation of entropy and mutual information

Science.gov (United States)

Lord, Warren M.; Sun, Jie; Bollt, Erik M.

2018-03-01

Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for a large sample size. These methods use geometrically regular local volume elements. This practice allows maximum localization of the volume elements, but can also induce a bias due to a poor description of the local geometry of the underlying probability measure. We introduce a new class of knn estimators that we call geometric knn estimators (g-knn), which use more complex local volume elements to better model the local geometry of the probability measures. As an example of this class of estimators, we develop a g-knn estimator of entropy and mutual information based on elliptical volume elements, capturing the local stretching and compression common to a wide range of dynamical system attractors. A series of numerical examples in which the thickness of the underlying distribution and the sample sizes are varied suggest that local geometry is a source of problems for knn methods such as the Kraskov-Stögbauer-Grassberger estimator when local geometric effects cannot be removed by global preprocessing of the data. The g-knn method performs well despite the manipulation of the local geometry. In addition, the examples suggest that the g-knn estimators can be of particular relevance to applications in which the system is large, but the data size is limited.

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

Science.gov (United States)

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks

Science.gov (United States)

Solanka, Lukas; van Rossum, Mark CW; Nolan, Matthew F

2015-01-01

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength. DOI: http://dx.doi.org/10.7554/eLife.06444.001 PMID:26146940

Long-Time Behavior and Critical Limit of Subcritical SQG Equations in Scale-Invariant Sobolev Spaces

Science.gov (United States)

Coti Zelati, Michele

2018-02-01

We consider the subcritical SQG equation in its natural scale-invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the regularity to the optimal level, derived by means of nonlinear lower bounds on the fractional Laplacian. This estimate appears to be new in the literature and allows a sharp use of the subcritical nature of the L^∞ bounds for this problem. As a by-product, we obtain attractors for weak solutions as well. Moreover, we study the critical limit of the attractors and prove their stability and upper semicontinuity with respect to the strength of the diffusion.

Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

Science.gov (United States)

Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.

2015-07-01

Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful

Measurement of DEM roughness using the local fractal dimension

OpenAIRE

Taud, Hind; Parrot, Jean-François

2008-01-01

Les relations entre les traits géomorphologiques et la rugosité de surface des Modèles Numériques de Terrain (MNT) ont été étudiées par l’intermédiaire de la géométrie fractale. La dimension fractale dans l’espace à trois dimensions est estimée localement sur la surface du MNT. Cette mesure se fait à l’aide d’une procédure dérivée de la technique du « comptage de boîtes ». Ce traitement a été appliqué sur deux zones tests choisies pour leurs différences lithologiques et tectoniques. La premiè...

Three-dimension reconstruction based on spatial light modulator

Energy Technology Data Exchange (ETDEWEB)

Deng Xuejiao; Zhang Nanyang; Zeng Yanan; Yin Shiliang; Wang Weiyu, E-mail: daisydelring@yahoo.com.cn [Huazhong University of Science and Technology (China)

2011-02-01

Three-dimension reconstruction, known as an important research direction of computer graphics, is widely used in the related field such as industrial design and manufacture, construction, aerospace, biology and so on. Via such technology we can obtain three-dimension digital point cloud from a two-dimension image, and then simulate the three-dimensional structure of the physical object for further study. At present, the obtaining of three-dimension digital point cloud data is mainly based on the adaptive optics system with Shack-Hartmann sensor and phase-shifting digital holography. Referring to surface fitting, there are also many available methods such as iterated discrete fourier transform, convolution and image interpolation, linear phase retrieval. The main problems we came across in three-dimension reconstruction are the extraction of feature points and arithmetic of curve fitting. To solve such problems, we can, first of all, calculate the relevant surface normal vector information of each pixel in the light source coordinate system, then these vectors are to be converted to the coordinates of image through the coordinate conversion, so the expectant 3D point cloud get arise. Secondly, after the following procedures of de-noising, repairing, the feature points can later be selected and fitted to get the fitting function of the surface topography by means of Zernike polynomial, so as to reconstruct the determinand's three-dimensional topography. In this paper, a new kind of three-dimension reconstruction algorithm is proposed, with the assistance of which, the topography can be estimated from its grayscale at different sample points. Moreover, the previous stimulation and the experimental results prove that the new algorithm has a strong capability to fit, especially for large-scale objects .

The Modal Dimension

Directory of Open Access Journals (Sweden)

Giluano Torrengo

2018-05-01

Full Text Available Space and time are two obvious candidates as dimensions of reality. Yet, are they the only two dimensions of reality? Famously, David Lewis maintained the doctrine of ―modal realism‖, the thesis that possible worlds exist and are entities as concrete as the actual world that we live in. In this paper, I will explore the idea that modality can be construed as a dimension along with space and time. However, although Lewis‘ modal realism is the main source of inspiration for this construal of modality, I will argue that something else is required for having a modal dimension.

Quasiperiodic transition to chaos in a plasma

International Nuclear Information System (INIS)

Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.

1993-01-01

The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos

Chaos and fractals an elementary introduction

CERN Document Server

Feldman, David P

2012-01-01

For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.

Dimensions of Creative Evaluation

DEFF Research Database (Denmark)

Christensen, Bo; Ball, Linden J.

2016-01-01

We examined evaluative reasoning taking place during expert ‘design critiques’. We focused on key dimensions of creative evaluation (originality, functionality and aesthetics) and ways in which these dimensions impact reasoning strategies and suggestions offered by experts for how the student could...... continue. Each dimension was associated with a specific underpinning ‘logic’ determining how these dimensions were evaluated in practice. Our analysis clarified how these dimensions triggered reasoning strategies such as running mental simulations or making design suggestions, ranging from ‘go...

Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions.

Science.gov (United States)

Vivek, Skanda; Kelleher, Colm P; Chaikin, Paul M; Weeks, Eric R

2017-02-21

Phase transitions significantly differ between 2D and 3D systems, but the influence of dimensionality on the glass transition is unresolved. We use microscopy to study colloidal systems as they approach their glass transitions at high concentrations and find differences between two dimensions and three dimensions. We find that, in two dimensions, particles can undergo large displacements without changing their position relative to their neighbors, in contrast with three dimensions. This is related to Mermin-Wagner long-wavelength fluctuations that influence phase transitions in two dimensions. However, when measuring particle motion only relative to their neighbors, two dimensions and three dimensions have similar behavior as the glass transition is approached, showing that the long-wavelength fluctuations do not cause a fundamental distinction between 2D and 3D glass transitions.

Multiple attractors and critical parameters and how to find them numerically: the right, the wrong and the gambling way

Science.gov (United States)

True, Hans

2013-03-01

In recent years, several authors have proposed 'easier numerical methods' to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are commented upon. I also address the questions when a linearisation is allowed and the curious fact that the hunting motion is more robust than the ideal stationary-state motion on the track. Concepts such as 'multiple attractors', 'subcritical and supercritical bifurcations', 'permitted linearisation', 'the danger of running at supercritical speeds' and 'chaotic motion' are addressed.

Sexual identity, attraction and behaviour in Britain: The implications of using different dimensions of sexual orientation to estimate the size of sexual minority populations and inform public health interventions.

Science.gov (United States)

Geary, Rebecca S; Tanton, Clare; Erens, Bob; Clifton, Soazig; Prah, Philip; Wellings, Kaye; Mitchell, Kirstin R; Datta, Jessica; Gravningen, Kirsten; Fuller, Elizabeth; Johnson, Anne M; Sonnenberg, Pam; Mercer, Catherine H

2018-01-01

Sexual orientation encompasses three dimensions: sexual identity, attraction and behaviour. There is increasing demand for data on sexual orientation to meet equality legislation, monitor potential inequalities and address public health needs. We present estimates of all three dimensions and their overlap in British men and women, and consider the implications for health services, research and the development and evaluation of public health interventions. Analyses of data from Britain's third National Survey of Sexual Attitudes and Lifestyles, a probability sample survey (15,162 people aged 16-74 years) undertaken in 2010-2012. A lesbian, gay or bisexual (LGB) identity was reported by 2·5% of men and 2·4% of women, whilst 6·5% of men and 11·5% of women reported any same-sex attraction and 5·5% of men and 6·1% of women reported ever experience of same-sex sex. This equates to approximately 547,000 men and 546,000 women aged 16-74 in Britain self-identifying as LGB and 1,204,000 men and 1,389,000 women ever having experience of same-sex sex. Of those reporting same-sex sex in the past 5 years, 28% of men and 45% of women identified as heterosexual. There is large variation in the size of sexual minority populations depending on the dimension applied, with implications for the design of epidemiological studies, targeting and monitoring of public health interventions and estimating population-based denominators. There is also substantial diversity on an individual level between identity, behaviour and attraction, adding to the complexity of delivering appropriate services and interventions.

Sexual identity, attraction and behaviour in Britain: The implications of using different dimensions of sexual orientation to estimate the size of sexual minority populations and inform public health interventions

Science.gov (United States)

Erens, Bob; Clifton, Soazig; Prah, Philip; Wellings, Kaye; Mitchell, Kirstin R.; Datta, Jessica; Gravningen, Kirsten; Fuller, Elizabeth; Johnson, Anne M.; Sonnenberg, Pam; Mercer, Catherine H.

2018-01-01

Background Sexual orientation encompasses three dimensions: sexual identity, attraction and behaviour. There is increasing demand for data on sexual orientation to meet equality legislation, monitor potential inequalities and address public health needs. We present estimates of all three dimensions and their overlap in British men and women, and consider the implications for health services, research and the development and evaluation of public health interventions. Methods Analyses of data from Britain’s third National Survey of Sexual Attitudes and Lifestyles, a probability sample survey (15,162 people aged 16–74 years) undertaken in 2010–2012. Findings A lesbian, gay or bisexual (LGB) identity was reported by 2·5% of men and 2·4% of women, whilst 6·5% of men and 11·5% of women reported any same-sex attraction and 5·5% of men and 6·1% of women reported ever experience of same-sex sex. This equates to approximately 547,000 men and 546,000 women aged 16–74 in Britain self-identifying as LGB and 1,204,000 men and 1,389,000 women ever having experience of same-sex sex. Of those reporting same-sex sex in the past 5 years, 28% of men and 45% of women identified as heterosexual. Interpretation There is large variation in the size of sexual minority populations depending on the dimension applied, with implications for the design of epidemiological studies, targeting and monitoring of public health interventions and estimating population-based denominators. There is also substantial diversity on an individual level between identity, behaviour and attraction, adding to the complexity of delivering appropriate services and interventions. PMID:29293516

Sexual identity, attraction and behaviour in Britain: The implications of using different dimensions of sexual orientation to estimate the size of sexual minority populations and inform public health interventions.

Directory of Open Access Journals (Sweden)

Rebecca S Geary

Full Text Available Sexual orientation encompasses three dimensions: sexual identity, attraction and behaviour. There is increasing demand for data on sexual orientation to meet equality legislation, monitor potential inequalities and address public health needs. We present estimates of all three dimensions and their overlap in British men and women, and consider the implications for health services, research and the development and evaluation of public health interventions.Analyses of data from Britain's third National Survey of Sexual Attitudes and Lifestyles, a probability sample survey (15,162 people aged 16-74 years undertaken in 2010-2012.A lesbian, gay or bisexual (LGB identity was reported by 2·5% of men and 2·4% of women, whilst 6·5% of men and 11·5% of women reported any same-sex attraction and 5·5% of men and 6·1% of women reported ever experience of same-sex sex. This equates to approximately 547,000 men and 546,000 women aged 16-74 in Britain self-identifying as LGB and 1,204,000 men and 1,389,000 women ever having experience of same-sex sex. Of those reporting same-sex sex in the past 5 years, 28% of men and 45% of women identified as heterosexual.There is large variation in the size of sexual minority populations depending on the dimension applied, with implications for the design of epidemiological studies, targeting and monitoring of public health interventions and estimating population-based denominators. There is also substantial diversity on an individual level between identity, behaviour and attraction, adding to the complexity of delivering appropriate services and interventions.

Interactive Dimensioning of Parametric Models

KAUST Repository

Kelly, T.

2015-06-22

We propose a solution for the dimensioning of parametric and procedural models. Dimensioning has long been a staple of technical drawings, and we present the first solution for interactive dimensioning: A dimension line positioning system that adapts to the view direction, given behavioral properties. After proposing a set of design principles for interactive dimensioning, we describe our solution consisting of the following major components. First, we describe how an author can specify the desired interactive behavior of a dimension line. Second, we propose a novel algorithm to place dimension lines at interactive speeds. Third, we introduce multiple extensions, including chained dimension lines, controls for different parameter types (e.g. discrete choices, angles), and the use of dimension lines for interactive editing. Our results show the use of dimension lines in an interactive parametric modeling environment for architectural, botanical, and mechanical models.

Estimation of soil water retention curve using fractal dimension ...

African Journals Online (AJOL)

The soil water retention curve (SWRC) is a fundamental hydraulic property majorly used to study flow transport in soils and calculate plant-available water. Since, direct measurement of SWRC is time-consuming and expensive, different models have been developed to estimate SWRC. In this study, a fractal-based model ...

E-Government Dimension

OpenAIRE

Rosiyadi, Didi; Suryana, Nana; Cahyana, Ade; Nuryani, Nuryani

2007-01-01

Makalah ini mengemukakan E-Government Dimension yang merupakan salah satu hasil TahapanPengumpulan Data, dimana tahapan ini adalah bagian dari penelitian kompetitif di Lembaga Ilmu PengetahuanIndonesia 2007 yang sekarang sedang dilakukan. Data E-Government Dimension ini didapatkan dari berbagaisumber yang meliputi E-Government beberapa Negara di dunia, E-Government yang dibangun oleh beberapapenyedia aplikasi E-Government. E-Government Dimension terdiri dari tiga dimensi yaitu DemocraticDimen...

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Directory of Open Access Journals (Sweden)

MC. Souza

Full Text Available Leaf area estimation is an important biometrical trait for evaluating leaf development and plant growth in field and pot experiments. We developed a non-destructive model to estimate the leaf area (LA of Vernonia ferruginea using the length (L and width (W leaf dimensions. Different combinations of linear equations were obtained from L, L2, W, W2, LW and L2W2. The linear regressions using the product of LW dimensions were more efficient to estimate the LA of V. ferruginea than models based on a single dimension (L, W, L2 or W2. Therefore, the linear regression “LA=0.463+0.676WL” provided the most accurate estimate of V. ferruginea leaf area. Validation of the selected model showed that the correlation between real measured leaf area and estimated leaf area was very high.

Sign rank versus Vapnik-Chervonenkis dimension

Science.gov (United States)

Alon, N.; Moran, Sh; Yehudayoff, A.

2017-12-01

This work studies the maximum possible sign rank of sign (N × N)-matrices with a given Vapnik-Chervonenkis dimension d. For d=1, this maximum is three. For d=2, this maximum is \\widetilde{\\Theta}(N1/2). For d >2, similar but slightly less accurate statements hold. The lower bounds improve on previous ones by Ben-David et al., and the upper bounds are novel. The lower bounds are obtained by probabilistic constructions, using a theorem of Warren in real algebraic topology. The upper bounds are obtained using a result of Welzl about spanning trees with low stabbing number, and using the moment curve. The upper bound technique is also used to: (i) provide estimates on the number of classes of a given Vapnik-Chervonenkis dimension, and the number of maximum classes of a given Vapnik-Chervonenkis dimension--answering a question of Frankl from 1989, and (ii) design an efficient algorithm that provides an O(N/log(N)) multiplicative approximation for the sign rank. We also observe a general connection between sign rank and spectral gaps which is based on Forster's argument. Consider the adjacency (N × N)-matrix of a Δ-regular graph with a second eigenvalue of absolute value λ and Δ ≤ N/2. We show that the sign rank of the signed version of this matrix is at least Δ/λ. We use this connection to prove the existence of a maximum class C\\subseteq\\{+/- 1\\}^N with Vapnik-Chervonenkis dimension 2 and sign rank \\widetilde{\\Theta}(N1/2). This answers a question of Ben-David et al. regarding the sign rank of large Vapnik-Chervonenkis classes. We also describe limitations of this approach, in the spirit of the Alon-Boppana theorem. We further describe connections to communication complexity, geometry, learning theory, and combinatorics. Bibliography: 69 titles.

More dimensions: Less entropy

International Nuclear Information System (INIS)

Kolb, E.W.; Lindley, D.; Seckel, D.

1984-01-01

For a cosmological model with d noncompact and D compact spatial dimensions and symmetry R 1 x S/sup d/ x S/sup D/, we calculate the entropy produced in d dimensions due to the compactification of D dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions

Quantitative estimation of defects from measurement obtained by remote field eddy current inspection

International Nuclear Information System (INIS)

Davoust, M.E.; Fleury, G.

1999-01-01

Remote field eddy current technique is used for dimensioning grooves that may occurs in ferromagnetic pipes. This paper proposes a method to estimate the depth and the length of corrosion grooves from measurement of a pick-up coil signal phase at different positions close to the defect. Grooves dimensioning needs the knowledge of the physical relation between measurements and defect dimensions. So, finite element calculations are performed to obtain a parametric algebraic function of the physical phenomena. By means of this model and a previously defined general approach, an estimate of groove size may be given. In this approach, algebraic function parameters and groove dimensions are linked through a polynomial function. In order to validate this estimation procedure, a statistical study has been performed. The approach is proved to be suitable for real measurements. (authors)

DIFFERENT DIMENSIONS OF TEAMS

OpenAIRE

Goparaju Purna SUDHAKAR

2013-01-01

Popularity of teams is growing in 21st Century. Organizations are getting their work done through different types of teams. Teams have proved that the collective performance is more than the sum of the individual performances. Thus, the teams have got different dimensions such as quantitative dimensions and qualitative dimensions. The Quantitative dimensions of teams such as team performance, team productivity, team innovation, team effectiveness, team efficiency, team decision making and tea...

A revised catalog of CfA galaxy groups in the Virgo/Great Attractor flow field

Science.gov (United States)

Nolthenius, Richard

1993-01-01

A new identification of groups and clusters in the CfAl Catalog of Huchra, et al. (1983) is presented, using a percolation algorithm to identify density enhancements. The procedure differs from that of the original Geller and Huchra (1983; GH) catalog in several important respects; galaxy distances are calculated from the Virgo-Great Attractor flow model of Faber and Burnstein (1988), the adopted distance linkage criteria is only approx. 1/4 as large as in the Geller and Huchra catalog, the sky link relation is taken from Nolthenius and White (1987), correction for interstellar extinction is included, and 'by-hand' adjustments to group memberships are made in the complex regions of Virgo/Coma I/Ursa Major and Coma/A1367 (to allow for varying group velocity dispersions and to trim unphysical 'spider arms'). Since flow model distances are poorly determined in these same regions, available distances from the IR Tully-Fisher planetary nebula luminosity function and surface brightness resolution methods are adopted if possible.

About the relationships among variables observed in the real world

Science.gov (United States)

Petkov, Boyan H.

2018-06-01

Since a stationary chaotic system is determined by nonlinear equations connecting its components, the appurtenance of two variables to such a system has been considered a sign of nontrivial relationships between them including also other quantities. These relationships could remain hidden for the approach usually employed in the research analyses, which is based on the extent of the correlation that characterises the dependence of one variable on the other. The appurtenance to the same system can be hypothesized if the topological features of the attractors reconstructed from two time series representing the evolution of the corresponding variables are close to each other. However, the possibility that both attractors represent different systems with similar behaviour cannot be excluded. For that reason, an approach allowing the reconstruction of the attractor by using jointly two time series was proposed and the conclusion about the common origin of the variables under study can be made if this attractor is topologically similar to those built separately from the two time series. In the present study, the features of the attractors were presented by the correlation dimension and the largest Lyapunov exponent and the proposed algorithm has been tested on numerically generated sequences obtained from various maps. It is believed that this approach could be used to reveal connections among the variables observed in experiments or field measurements.

Numerical explorations of R. M. Goodwin's business cycle model.

Science.gov (United States)

Jakimowicz, Aleksander

2010-01-01

Goodwin's model, which was formulated in , still attracts economists' attention. The model possesses numerous interesting properties that have been discovered only recently due to the development of the chaos theory and the complexity theory. The first numerical explorations of the model were conducted in the early s by Strotz, McAnulty and Naines (1953). They discovered the coexistence of attractors that are well-known today, two properties of chaotic systems: the sensitive dependence on the initial conditions and the sensitive dependence on parameters. The occurrence of periodic and chaotic attractors is dependent on the value of parameters in a system. In case of certain parametric values fractal basin boundaries exist which results in enormous system sensitivity to external noise. If periodic attractors are placed in the neighborhood of the fractal basin boundaries, then even a low external noise can move the trajectory into the region in which the basin's structure is tangled. This leads to a kind of movement that resembles a chaotic movement on a strange attractor. In Goodwin's model, apart from typical chaotic behavior, there exists yet another kind of complex movements - transient chaotic behavior that is caused by the occurrence of invariant chaotic sets that are not attracting. Such sets are represented by chaotic saddles. Some of the latest observation methods of trajectories lying on invariant chaotic sets that are not attracting are straddle methods. This article provides examples of the basin boundary straddle trajectory and the saddle straddle trajectory. These cases were studied by Lorenz and Nusse (2002). I supplement the results they acquired with calculations of capacity dimension and correlation dimension.

Correlation dimension of financial market

Science.gov (United States)

Nie, Chun-Xiao

2017-05-01

In this paper, correlation dimension is applied to financial data analysis. We calculate the correlation dimensions of some real market data and find that the dimensions are significantly smaller than those of the simulation data based on geometric Brownian motion. Based on the analysis of the Chinese and US stock market data, the main results are as follows. First, by calculating three data sets for the Chinese and US market, we find that large market volatility leads to a significant decrease in the dimensions. Second, based on 5-min stock price data, we find that the Chinese market dimension is significantly larger than the US market; this shows a significant difference between the two markets for high frequency data. Third, we randomly extract stocks from a stock set and calculate the correlation dimensions, and find that the average value of these dimensions is close to the dimension of the original set. In addition, we analyse the intuitional meaning of the relevant dimensions used in this paper, which are directly related to the average degree of the financial threshold network. The dimension measures the speed of the average degree that varies with the threshold value. A smaller dimension means that the rate of change is slower.

Estimation of EuroQol 5-Dimensions health status utility values in hereditary angioedema.

Science.gov (United States)

Aygören-Pürsün, Emel; Bygum, Anette; Beusterien, Kathleen; Hautamaki, Emily; Sisic, Zlatko; Boysen, Henrik B; Caballero, Teresa

2016-01-01

To estimate health status utility (preference) weights for hereditary angioedema (HAE) during an attack and between attacks using data from the Hereditary Angioedema Burden of Illness Study in Europe (HAE-BOIS-Europe) survey. Utility measures quantitatively describe the net impact of a condition on a patient's life; a score of 0.0 reflects death and 1.0 reflects full health. The HAE-BOIS-Europe was a cross-sectional survey conducted in Spain, Germany, and Denmark to assess the real-world experience of HAE from the patient perspective. Survey items that overlapped conceptually with the EuroQol 5-Dimensions (EQ-5D) domains (pain/discomfort, mobility, self-care, usual activities, and anxiety/depression) were manually crosswalked to the corresponding UK population-based EQ-5D utility weights. EQ-5D utilities were computed for each respondent in the HAE-BOIS-Europe survey for acute attacks and between attacks. Overall, a total of 111 HAE-BOIS-Europe participants completed all selected survey items and thus allowed for computation of EQ-5D-based utilities. The mean utilities for an HAE attack and between attacks were 0.44 and 0.72, respectively. Utilities for an acute attack were dependent on the severity of pain of the last attack (0.61 for no pain or mild pain, 0.47 for moderate pain, and 0.08 for severe pain). There were no significant differences across countries. Mean utilities derived from the study approach compare sensibly with other disease states for both acute attacks and between attacks. The impacts of HAE translate into substantial health status disutilities associated with acute attacks as well as between attacks, documenting that the detrimental effects of HAE are meaningful from the patient perspective. Results were consistent across countries with regard to pain severity and in comparison to similar disease states. The results can be used to raise awareness of HAE as a serious disease with wide-ranging personal and social impacts.

Some Convex Functions Based Measures of Independence and Their Application to Strange Attractor Reconstruction

Directory of Open Access Journals (Sweden)

Kazuyuki Aihara

2011-04-01

Full Text Available The classical information-theoretic measures such as the entropy and the mutual information (MI are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO and the quasientropy (QE as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI. A quality factor (QF is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.

Deconstructing dimensions

International Nuclear Information System (INIS)

Cohen, A.G.

2003-01-01

Extra-dimensional physics is realized as the low-energy limit of lower-dimensional gauge theories. This 'deconstruction' of dimensions provides a UV completion of higher-dimensional theories, and has been used to investigate the physics of extra-dimensions. This technique has also led to a variety of interesting phenomenological applications, especially a new class of models of electroweak superconductivity, called the 'little Higgs'. (author)

Characterizing adult human nasal airway dimensions

International Nuclear Information System (INIS)

Guilmette, R.A.; Griffith, W.C.

1994-01-01

Respiratory tract models used in calculating radiation dose from exposure to inhaled radioactive aerosols have only recently focused attention on the importance of the nasal airways (NAs). Because the NAs are the first tissues of the respiratory tract available for aerosol deposition in normally nose-breathing people, any deposition of aerosol in this anatomical structure will reduce the amounts available to be deposited in the remainder of the respiratory tract. Thus, uncertainties in estimating the deposition fractions in the NAs will propagate throughout the remainder of the respiratory tract, creating errors in the calculated dose estimates. Additionally, there is evidence that the NAs are also at risk for induction of cancer from exposure to certain occupational aerosols such as wood dust, leather dust, chromium, and nickel. The purpose of this investigation was to conduct an anatomical study to assess the variabilities in NA dimensions

Dimension yields from short logs of low-quality hardwood trees.

Science.gov (United States)

Howard N. Rosen; Harold A. Stewart; David J. Polak

1980-01-01

Charts are presented for determining yields of 4/4 dimension cuttings from short hardwood logs of aspen, soft maple, black cherry, yellow-poplar, and black walnut for several cutting grades and bolt sizes. Cost comparisons of short log and standard grade mixes show sizes. Cost comparisons of short log and standard grade mixes show the estimated least expensive...

Splitting in large dimension and infrared estimates. II. Moment inequalities

Science.gov (United States)

Helffer, B.

1998-02-01

This is the continuation of notes written for the NATO-ASI conference in Il Ciocco (September 96) consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the Schrödinger operator H and the proof of infrared estimates for quantities attached to Gaussian-type measures. These notes were mainly reporting on the "old" contributions of Dyson, Fröhlich, Glimm, Jaffe, Lieb, Simon, and Spencer (in the 1970s) in connection with more recent contributions of Pastur, Khoruzhenko, Barbulyak, and Kondrat'ev which treat in general more sophisticated models. Here we concentrate on the simplest model related to field theory and extend the results of Barbulyak and Kondrat'ev by mixing ideas coming from Pastur and Khozurenko related to the use of Bogolyubov's inequality with classical inequalities due to Ginibre, Lebowitz, Sokal, and others, or, in the case when the temperature T is zero, by applying rather elementary estimates on Schrödinger operators, in order to find lower bounds for second-order moments attached to the measure φ⟼Trφ exp-βH/Tr exp-βH with β=1/T. This question was "left to the reader" in lectures given by J. Fröhlich in 1976 [Acta Phys. Austriaca, Suppl. XV, 133-269 (1976)], but we think that it is worthwhile to do this "homework" carefully.

Dimension of linear models

DEFF Research Database (Denmark)

Høskuldsson, Agnar

1996-01-01

Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four of these cri......Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....

Dimension reduction of frequency-based direct Granger causality measures on short time series.

Science.gov (United States)

Siggiridou, Elsa; Kimiskidis, Vasilios K; Kugiumtzis, Dimitris

2017-09-01

The mainstream in the estimation of effective brain connectivity relies on Granger causality measures in the frequency domain. If the measure is meant to capture direct causal effects accounting for the presence of other observed variables, as in multi-channel electroencephalograms (EEG), typically the fit of a vector autoregressive (VAR) model on the multivariate time series is required. For short time series of many variables, the estimation of VAR may not be stable requiring dimension reduction resulting in restricted or sparse VAR models. The restricted VAR obtained by the modified backward-in-time selection method (mBTS) is adapted to the generalized partial directed coherence (GPDC), termed restricted GPDC (RGPDC). Dimension reduction on other frequency based measures, such the direct directed transfer function (dDTF), is straightforward. First, a simulation study using linear stochastic multivariate systems is conducted and RGPDC is favorably compared to GPDC on short time series in terms of sensitivity and specificity. Then the two measures are tested for their ability to detect changes in brain connectivity during an epileptiform discharge (ED) from multi-channel scalp EEG. It is shown that RGPDC identifies better than GPDC the connectivity structure of the simulated systems, as well as changes in the brain connectivity, and is less dependent on the free parameter of VAR order. The proposed dimension reduction in frequency measures based on VAR constitutes an appropriate strategy to estimate reliably brain networks within short-time windows. Copyright © 2017 Elsevier B.V. All rights reserved.

The fourth dimension

CERN Document Server

Rucker, Rudy

2014-01-01

""This is an invigorating book, a short but spirited slalom for the mind."" - Timothy Ferris, The New York Times Book Review ""Highly readable. One is reminded of the breadth and depth of Hofstadter's Gödel, Escher, Bach."" - Science""Anyone with even a minimal interest in mathematics and fantasy will find The Fourth Dimension informative and mind-dazzling... [Rucker] plunges into spaces above three with a zest and energy that is breathtaking."" - Martin Gardner ""Those who think the fourth dimension is nothing but time should be encouraged to read The Fourth Dimension, along with anyone else

Methods for determining the preatmospheric dimensions of meteorites

Science.gov (United States)

Ustinova, G. K.; Alekseev, V. A.; Lavrukhina, A. K.

1988-10-01

Methods are proposed for the determination of the preatmospheric size of a meteorite on the basis of data on its cosmogenic radionuclides. Optimal conditions for the application of each of these methods are presented together with the demonstration of their effectiveness. Estimates of relative dimensions determined by these methods are presented for the Harleton, St. Severin, Lost City, Peace River, Pribram, Dhajala, Innisfree, Bruderheim, Ehole, and Gorlovka chondrites and for the Iardymly, Boguslavka, Treysa, and Sikhote-Alin' iron meteorites.

Effective dysphonia detection using feature dimension reduction and kernel density estimation for patients with Parkinson's disease.

Directory of Open Access Journals (Sweden)

Shanshan Yang

Full Text Available Detection of dysphonia is useful for monitoring the progression of phonatory impairment for patients with Parkinson's disease (PD, and also helps assess the disease severity. This paper describes the statistical pattern analysis methods to study different vocal measurements of sustained phonations. The feature dimension reduction procedure was implemented by using the sequential forward selection (SFS and kernel principal component analysis (KPCA methods. Four selected vocal measures were projected by the KPCA onto the bivariate feature space, in which the class-conditional feature densities can be approximated with the nonparametric kernel density estimation technique. In the vocal pattern classification experiments, Fisher's linear discriminant analysis (FLDA was applied to perform the linear classification of voice records for healthy control subjects and PD patients, and the maximum a posteriori (MAP decision rule and support vector machine (SVM with radial basis function kernels were employed for the nonlinear classification tasks. Based on the KPCA-mapped feature densities, the MAP classifier successfully distinguished 91.8% voice records, with a sensitivity rate of 0.986, a specificity rate of 0.708, and an area value of 0.94 under the receiver operating characteristic (ROC curve. The diagnostic performance provided by the MAP classifier was superior to those of the FLDA and SVM classifiers. In addition, the classification results indicated that gender is insensitive to dysphonia detection, and the sustained phonations of PD patients with minimal functional disability are more difficult to be correctly identified.

Krull dimension in modal logic

NARCIS (Netherlands)

Bezhanishvili, G.; Bezhanishvili, N.; Lucero-Bryan, J.; van Mill, J.

2017-01-01

We develop the theory of Krull dimension for S4-algebras and Heyting algebras. This leads to the concept of modal Krull dimension for topological spaces. We compare modal Krull dimension to other well-known dimension functions, and show that it can detect differences between topological spaces that

Discovering Digital Signage System Opportunities as Crowd Attractor in Public Spaces: A Study in Charge Gratis Service

Directory of Open Access Journals (Sweden)

Ahmad Faisal Choiril Anam Fathoni

2016-07-01

Full Text Available Article presented a research about the "Charge Gratis" service that included digital signage, along with free charging device as the crowd attractors in the public space. The main focus of this research was about media display embedded in the uniform of a sales promotion person who displays ads from the advertiser using the qualitative method, through the interview with some expert sources many fields. Article described several possibilities that can be worked in the use of digital signage so that it can be used as a reference in maximizing digital signage in public spaces. It finds that Digital signage is not just functioned as like any other media, but also the awaken interaction and also enhance shopping experiences. The expert sources divide this media display functions into three categories, which is a media information, media entertainment, and media education. 

Optimal complex exponentials BEM and channel estimation in doubly selective channel

International Nuclear Information System (INIS)

Song, Lijun; Lei, Xia; Yu, Feng; Jin, Maozhu

2016-01-01

Over doubly selective channel, the optimal complex exponentials BEM (CE-BEM) is required to characterize the transmission in transform domain in order to reducing the huge number of the estimated parameters during directly estimating the impulse response in time domain. This paper proposed an improved CE-BEM to alleviating the high frequency sampling error caused by conventional CE-BEM. On the one hand, exploiting the improved CE-BEM, we achieve the sampling point is in the Doppler spread spectrum and the maximum sampling frequency is equal to the maximum Doppler shift. On the other hand we optimize the function and dimension of basis in CE-BEM respectively ,and obtain the closed solution of the EM based channel estimation differential operator by exploiting the above optimal BEM. Finally, the numerical results and theoretic analysis show that the dimension of basis is mainly depend on the maximum Doppler shift and signal-to-noise ratio (SNR), and if fixing the number of the pilot symbol, the dimension of basis is higher, the modeling error is smaller, while the accuracy of the parameter estimation is reduced, which implies that we need to achieve a tradeoff between the modeling error and the accuracy of the parameter estimation and the basis function influences the accuracy of describing the Doppler spread spectrum after identifying the dimension of the basis.

Performance pay, sorting and the dimensions of job satisfaction

OpenAIRE

C Green; J S Heywood

2007-01-01

This paper investigates the influence of performance related pay on several dimensions of job satisfaction. In cross-sectional estimates, performance related pay is associated with increased overall satisfaction, satisfaction with pay, satisfaction with job security and satisfaction with hours. It appears to be negatively associated with satisfaction with the work itself. Yet, after accounting for worker fixed-effects, the positive associations remain and the negative association vanishes. Th...

The geometry of chaotic dynamics — a complex network perspective

Science.gov (United States)

Donner, R. V.; Heitzig, J.; Donges, J. F.; Zou, Y.; Marwan, N.; Kurths, J.

2011-12-01

Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ɛ-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ɛ-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that ɛ-recurrence networks exhibit an important link between dynamical systems and graph theory.

Religiosity dimensions and subjective health status in Greek students.

Science.gov (United States)

Kioulos, K T; Bergiannaki, J D; Glaros, A; Vassiliadou, M; Alexandri, Z; Papadimitriou, G

2015-01-01

The quest for existential meaning constitutes a universal phenomenon traditionally manifested in official religions (religiosity) or personal modes of transcendence (spirituality). Religiosity and spirituality have been found to be associated with a variety of mental health and illness parameters. In the last decades there is an increasing number of publications with interesting results on the relationship between religiosity and mental health, both on a theoretical and a clinical level. Recent research suggests the presence of clinically important interactions between religious beliefs and mental health, although the exact nature of the associations remains unclear. The aim of the present study is to investigate subjective health status in relation to specific dimensions of religiosity and spirituality in Greek students; 202 students of the faculty of Theology of the University of Athens were interviewed using the Brief Multidimensional Measurement of Religiousness/Spirituality (BMMRS), which assesses the dimensions of "daily spiritual experiences", "meaning", "values/beliefs", "forgiveness", "private religious practices", "religious/spiritual coping", "religious support", "religious/ spiritual history", "commitment", "organizational religiousness", and "religious preferences". Subjective health status was measured by the General Health Questionnaire (GHQ-28) which examines four areas of health in the following sub-scales: (a) somatic symptoms, (b) anxiety and insomnia, (c) social dysfunction and (d) severe depression. Pearson correlations coefficients and linear regression analyses were used to estimate the associations of GHQ-28 subscales with religiosity dimensions. High scores in each dimension of BMMRS corresponded to a low level of religiosity. The dimension of "daily spiritual experiences" was positively correlated with the subscales of anxiety/ insomnia, social dysfunction and severe depression, while the dimension of "values/beliefs" with social

User Experience Dimensions

DEFF Research Database (Denmark)

Lykke, Marianne; Jantzen, Christian

2016-01-01

The present study develops a set of 10 dimensions based on a systematic understanding of the concept of experience as a holistic psychological. Seven of these are derived from a psychological conception of what experiencing and experiences are. Three supplementary dimensions spring from the obser...

ANTHROPOLOGY DIMENSIONS AS INDEPENDENT AEROBIC ENDURANCE

Directory of Open Access Journals (Sweden)

Ratko Pavlović

2009-11-01

Full Text Available Endurance as human capability is treated in two ways. Some authors define it as mobility capability, while others deny this theory. The denying of this theory lies in attitude that endurance is saturated with psychological factors (motivation and cardio- vascular factors as well and is often identified with aero power, typical dimension of fun- ctional diagnostics. Having that in mind this research enabled the obtaining of necessary informations which could contribute to the clearing up of these uncoordinated opinions. The research included 110 student of the III year Phisical Education in East Sarajevo, male gender. Nine (9 predictors has been applied (4 variables for mobility space estima- te, 5 variables for morphology and functional space estimate and variable used for the estimate of endurance race 1500m. Obtained results confirmed statistical significance of two functional capability variable of Harvard step test, Margarija test and mobility variable race 4x15 meters with the race results.

Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis

Science.gov (United States)

Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua

Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.

Study of the attractor structure of an agent-based sociological model

Energy Technology Data Exchange (ETDEWEB)

Timpanaro, Andre M; Prado, Carmen P C, E-mail: timpa@if.usp.br, E-mail: prado@if.usp.br [Instituto de Fisica da Universidade de Sao Paulo, Sao Paulo (Brazil)

2011-03-01

The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabasi-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.

Effect of the Great Attractor on the cosmic microwave background radiation

Energy Technology Data Exchange (ETDEWEB)

Bertschinger, E [Massachusetts Inst. of Tech., Cambridge, MA (USA). Dept. of Physics; Gorski, K M [Los Alamos National Lab., NM (USA); Dekel, A [Hebrew Univ., Jerusalem (Israel). Racah Inst. of Physics

1990-06-07

ANISOTROPY in the cosmic microwave background radiation (CMB) is expected as a result of fluctuations in gravitational potential caused by large-scale structure in the Universe. The background radiation is redshifted as it climbs out of gravitational wells. Here we present a map of the anisotropy in CMB temperature {Delta}T/T of our region of the Universe as viewed by a distant observer, predicted on the basis of the gravitational potential field. We calculate this field in the vicinity of the Local Group of galaxies from the observed peculiar (non-Hubble) velocities of galaxies, under the assumption that the peculiar motions are induced by gravity. If the cosmological density parameter {Omega} is 1, the gravitational potential field of the Great Attractor and surrounding regions produces a maximum Sachs-Wolfe anisotropy of {Delta}T/T=(1.7{plus minus}0.3) x 10{sup -5} on an angular scale of 1deg. Doppler and adiabatic contributions to this anisotropy are expected to be somewhat larger. If similar fluctuations in the gravitational potential are present elsewhere in the Universe, the anisotropy present when the CMB was last scattered should be visible from the Earth, and should be detectable in current experiments. A fundamental test of whether gravity is responsible for the generation of structure in the Universe can be made by looking for the imprint in the CMB of deep potential wells similar to those found in our neighbourhood, (author).

Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation

Directory of Open Access Journals (Sweden)

ELNAZ Rezaei abajelu

2017-03-01

Full Text Available Introduction: Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks. Fractal models with two subset of two (solid and pore and three phases (solid, pore and soil fractal (PSF are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD and soil moisture retention curve (SWRC. The main objective of this study was to evaluate different fractal models to estimate the Ksparameter. Materials and Methods: The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996, Hunt and Gee (2002, Bird et al. (2000, Huang and Zhang (2005, Tyler and Wheatcraft (1990, Kutlu et al. (2008, Sepaskhah and Tafteh (2013.Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension by seven fractal models (Table 2.Sensitivity analysis of Rawls model was assessed by making changes±10%, ±20% and±30%(in input parameters

Two-Dimensional DOA Estimation in Compressed Sensing with Compressive-Reduced Dimension-lp-MUSIC

Directory of Open Access Journals (Sweden)

Weijian Si

2015-01-01

Full Text Available This paper presents a novel two-dimensional (2D direction of arrival (DOA estimation method in compressed sensing (CS to remove the estimation failure problem and achieve superior performance. The proposed method separates the steering vector into two parts to construct two corresponding noise subspaces by introducing electric angles. Then, electric angles are estimated based on the constructed noise subspaces. In order to estimate the azimuth and elevation angles in terms of estimates of electric angles, arc-tangent operations are exploited. The arc-tangent is a one-to-one function and allows the value of the argument to be larger than unity so that the proposed method never fails. The proposed method can avoid pair matching to reduce the computational complexity and extend the number of snapshots to improve performance. Simulation results show that the proposed method can avoid estimation failure occurrence and has superior performance as compared to existing methods.

On dynamics analysis of a new chaotic attractor

International Nuclear Information System (INIS)

Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin

2008-01-01

In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation

On discriminant analysis techniques and correlation structures in high dimensions

DEFF Research Database (Denmark)

Clemmensen, Line Katrine Harder

This paper compares several recently proposed techniques for performing discriminant analysis in high dimensions, and illustrates that the various sparse methods dier in prediction abilities depending on their underlying assumptions about the correlation structures in the data. The techniques...... the methods in two: Those who assume independence between the variables and thus use a diagonal estimate of the within-class covariance matrix, and those who assume dependence between the variables and thus use an estimate of the within-class covariance matrix, which also estimates the correlations between...... variables. The two groups of methods are compared and the pros and cons are exemplied using dierent cases of simulated data. The results illustrate that the estimate of the covariance matrix is an important factor with respect to choice of method, and the choice of method should thus be driven by the nature...

Relaxing to Three Dimensions

CERN Document Server

CERN. Geneva

2006-01-01

Extra dimensions of space might be present in our universe. If so, we want to know 'How do dimensions hide?' and 'Why are three dimensions special?' I'll give potential answers to both these questions in the context of localized gravity. Organiser(s): L. Alvarez-Gaume / PH-THNote: * Tea & coffee will be served at 16:00. Talk is broadcasted in Council Chamber

Dimension and extensions

CERN Document Server

Aarts, JM

1993-01-01

Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a...