Raza, Muhammad; Myrzakulov, Kairat; Momeni, Davood; Myrzakulov, Ratbay
2016-05-01
In this paper,we investigate the mathematical modeling for the cosmological attractors propagated in mimetic gravity upon which an interacting dark energy-dark matter is supposed to be existed. The average value of the interaction of these percentages, namely Γ i say, may be used to investigate generally the modeling of an attractor; the actual value could only be determined by data in any particular case. We have seen, for example, that it was led to investigate the subject of initially invariant submanifolds.
Goldstein, Kevin; Nampuri, Suresh
2014-01-01
The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions.
International Nuclear Information System (INIS)
We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in toroidally compactified heterotic string theory
Recurrences of strange attractors
Indian Academy of Sciences (India)
E J Ngamga; A Nandi; R Ramaswamy; M C Romano; M Thiel; J Kurths
2008-06-01
The transitions from or to strange nonchaotic attractors are investigated by recurrence plot-based methods. The techniques used here take into account the recurrence times and the fact that trajectories on strange nonchaotic attractors (SNAs) synchronize. The performance of these techniques is shown for the Heagy-Hammel transition to SNAs and for the fractalization transition to SNAs for which other usual nonlinear analysis tools are not successful.
International Nuclear Information System (INIS)
This paper deals with attractors of generic dynamical systems. We introduce the notion of ε-invisible set, which is an open set of the phase space in which almost all orbits spend on average a fraction of time no greater than ε. For extraordinarily small values of ε (say, smaller than 2−100), these are large neighbourhoods of some parts of the attractors in the phase space which an observer virtually never sees when following a generic orbit. For any n ≥ 100, we construct a set Qn in the space of skew products over a solenoid with the fibre a circle having the following properties. Any map from Qn is a structurally stable diffeomorphism; the Lipschitz constants of the map and its inverse are no greater than L (where L is a universal constant that does not depend on n, say L n has a 2−n-invisible part of its attractor, whose size is comparable to that of the whole attractor. The set Qn is a ball of radius O(n−2) in the space of skew products with the C1 metric. It consists of structurally stable skew products. Small perturbations of these skew products in the space of all diffeomorphisms still have attractors with the same properties. Thus for all such perturbations, a sizable portion of the attractor is almost never visited by generic orbits and is practically never seen by the observer
Wiegerinck, Wim; Schoenaker, Christiaan; Duane, Gregory
2016-04-01
Recently, methods for model fusion by dynamically combining model components in an interactive ensemble have been proposed. In these proposals, fusion parameters have to be learned from data. One can view these systems as parametrized dynamical systems. We address the question of learnability of dynamical systems with respect to both short term (vector field) and long term (attractor) behavior. In particular we are interested in learning in the imperfect model class setting, in which the ground truth has a higher complexity than the models, e.g. due to unresolved scales. We take a Bayesian point of view and we define a joint log-likelihood that consists of two terms, one is the vector field error and the other is the attractor error, for which we take the L1 distance between the stationary distributions of the model and the assumed ground truth. In the context of linear models (like so-called weighted supermodels), and assuming a Gaussian error model in the vector fields, vector field learning leads to a tractable Gaussian solution. This solution can then be used as a prior for the next step, Bayesian attractor learning, in which the attractor error is used as a log-likelihood term. Bayesian attractor learning is implemented by elliptical slice sampling, a sampling method for systems with a Gaussian prior and a non Gaussian likelihood. Simulations with a partially observed driven Lorenz 63 system illustrate the approach.
Hidden attractors in dynamical systems
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.
Bellucci, S; Marrani, A
2008-01-01
We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attrac...
Fermions, wigs, and attractors
Energy Technology Data Exchange (ETDEWEB)
Gentile, L.G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Grassi, P.A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); INFN, Gruppo Collegato di Alessandria, Sezione di Torino (Italy); Marrani, A., E-mail: alessio.marrani@fys.kuleuven.be [ITF KU Leuven, Celestijnenlaan 200D, 3001 Leuven (Belgium); Mezzalira, A., E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique Université Libre de Bruxelles, C.P. 231, 1050 Bruxelles (Belgium)
2014-05-01
We compute the modifications to the attractor mechanism due to fermionic corrections. In N=2,D=4 supergravity, at the fourth order, we find terms giving rise to new contributions to the horizon values of the scalar fields of the vector multiplets.
Dimension of chaotic attractors
Energy Technology Data Exchange (ETDEWEB)
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
Attractors, Universality and Inflation
Downes, Sean; Sinha, Kuver
2012-01-01
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 an inverse cubic power law. 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.
Chaotic attractors with separated scrolls
Energy Technology Data Exchange (ETDEWEB)
Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr [Department of Electrical Engineering, Higher Institute of Applied Sciences and Technology of Sousse, Sousse (Tunisia)
2015-07-15
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.
Attractor comparisons based on density
International Nuclear Information System (INIS)
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
Inflationary Attractor from Tachyonic Matter
Guo, Z K; Cai, R G; Zhang, Y Z; Guo, Zong-Kuan; Piao, Yun-Song; Cai, Rong-Gen; Zhang, Yuan-Zhong
2003-01-01
We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behaviour of the tachyonic inflation using the Hamilton-Jacobi formalism. We else obtain analytical approximations to the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial non-vanishing momentum does not prevent the onset of inflation. The slow-rolling solution is an attractor.
Inflationary attractor from tachyonic matter
Guo, Zong-Kuan; Piao, Yun-Song; Cai, Rong-Gen; Zhang, Yuan-Zhong
2003-08-01
We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behavior of tachyonic inflation using the Hamilton-Jacobi formalism. We also obtain analytical approximations for the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial nonvanishing momentum does not prevent the onset of inflation. The slow-rolling solution is an attractor.
Inflation, Universality and Attractors
Scalisi, Marco
2016-01-01
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic K\\"ahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly...
Moduli Backreaction on Inflationary Attractors
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.
Chaos, turbulence and strange attractors
International Nuclear Information System (INIS)
Using the turbulence example, the author recalls the two different conceptions of the nature of an erratic regime: the one in which a great number of elementary events are concerned (Landau) and the other one in which, on the contrary, a few number of elementary events are concerned (Ruelle and Takens). The last type of erratic comportment has a deterministic origin and is pointed by the adjective chaotic. Phase space for a dynamic system is presented and so the attractor nation. Chaos and notion of sensitiveness to initial conditions are defined. In scrutining the geometry of an attractor corresponding to a chaotic regime, the notion of strange attractor is shown. Some experiments results are given as illustration. Application field is recalled: for example, studies on hamiltonian chaos are made at DRFC (Department of research on controlled fusion at CEA) in relation with plasma instabilities
Inflationary attractors and their measures
International Nuclear Information System (INIS)
Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We clarify some issues regarding the Hamiltonian dynamics of a flat Friedmann–Lemaître–Robertson–Walker cosmology coupled to a massive scalar field. In particular we show that the focusing of the Liouville measure on attractor solutions is recovered by properly dealing with a gauge degree of freedom related to the rescaling of the spatial volume. Furthermore, we show how the Liouville measure formulated on a surface of constant Hubble rate, together with the assumption of constant a priory probability, induces a non-uniform probability distribution function on any other surfaces of other Hubble rates. The attractor behaviour is seen through the focusing of this function on a narrow range of physical observables. This qualitative behaviour is robust under change of potential and underlying measure. One can then conclude that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem for inflationary dynamics. (fast track communications)
Intermittent control of coexisting attractors.
Liu, Yang; Wiercigroch, Marian; Ing, James; Pavlovskaia, Ekaterina
2013-06-28
This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method. PMID:23690639
Unstable attractors induce perpetual synchronization and desynchronization.
Timme, Marc; Wolf, Fred; Geisel, Theo
2003-03-01
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters. PMID:12675444
Lattice Structures for Attractors I
Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M.
2013-01-01
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a foundation for the development of algorithms to manipulate these structures computationally.
Attractors for Nonautonomous Parabolic Equations without Uniqueness
Directory of Open Access Journals (Sweden)
Nguyen Dinh Binh
2010-01-01
Full Text Available Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connectedness of the uniform global attractor.
Dark Energy from $\\alpha$-Attractors
Linder, Eric V
2015-01-01
A class of inflation theories called $\\alpha$-attractors has been investigated recently with interesting properties interpolating between quadratic potentials, the Starobinsky model, and an attractor limit. Here we examine their use for late time cosmic acceleration. We generalize the class and demonstrate how it can interpolate between thawing and freezing dark energy, and reduce the fine tuning of initial conditions, allowing $w\\approx-1$ for a prolonged period or as a de Sitter attractor.
Inflation as AN Attractor in Scalar Cosmology
Kim, Hyeong-Chan
2013-06-01
We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann-Robertson-Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton-Jacobi equation solving the field equations. The equation relates a solution "generating function" with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, V0>0. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, λ<9V0/16. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the quasi-attractor property disappears if the potential is modified. On the whole, the appearance of the eternal inflation is not rare in scalar cosmology in the presence of an attractor.
Black Hole Attractors in Extended Supergravity
Ferrara, Sergio
2007-01-01
We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities, reporting some recent advances on the moduli spaces associated to BPS and non-BPS attractor solutions supported by charge orbits with non-compact stabilizers.
Strange attractor simulated on a quantum computer
M. Terraneo; Georgeot, B.; D.L. Shepelyansky
2002-01-01
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.
Tetrapterous butterfly attractors in modified Lorenz systems
International Nuclear Information System (INIS)
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.
Wild attractors and thermodynamic formalism
Bruin, Henk
2012-01-01
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family $f_\\lambda$ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential $\\phi_t = -t\\log|f'_\\lambda|$, there is a unique phase transition at some $t_1 \\le 1$, and the pressure $P(\\phi_t)$ is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a non-analytic $C^\\infty$ curve (with all derivatives equal to 0 at $t_1 < 1$) at the emergence of a wild attractor, whereas the phase transition at $t_1 = 1$ can be of any finite order for those $\\lambda$ for which $f_\\lambda$ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of th...
Strange attractors in rattleback dynamics
Energy Technology Data Exchange (ETDEWEB)
Borisov, Aleksei V; Mamaev, Ivan S [Institute of Computer Science, Izhevsk (Russian Federation)
2003-04-30
This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters. (methodological notes)
Decaying turbulence and developing chaotic attractors
Bershadskii, A
2016-01-01
Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is shown that, unlike the case of statistically stationary homogeneous isotropic turbulence, the attractor associated with rotational symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local dynamics in an intermediate stage of the decay, because the attractor associated with translational symmetry (and controlled by Birkhoff-Saffman integral) is still not developed enough. The DNS data have been used in order to support this conclusion.
The Lorentz Attractor and Other Attractors in the Economic System of a Firm
International Nuclear Information System (INIS)
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
Global Attractors for a Nonclassical Diffusion Equation
Institute of Scientific and Technical Information of China (English)
Chun You SUN; Su Yun WANG; Cheng Kui ZHONG
2007-01-01
We prove the existence of global attractors in H10 (Ω) for a nonclassical diffusion equation.Two types of nonlinearity f are considered: one is the critical exponent, and the other is the polynomial growth of arbitrary order.
Singular-hyperbolic attractors are chaotic
Araujo, Vitor; Pacifico, Maria Jose; Pujals, Enrique; Viana, Marcelo
2005-01-01
We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their orbits coincide. Secondly, there exists a physical (or Sinai-Ruelle-Bowen) measure supported on the attractor whose ergodic basin covers a full Lebesgue (volume) measure subset of the topological basin of attraction. Moreover this measure has absolutely contin...
A plethora of strange nonchaotic attractors
Indian Academy of Sciences (India)
Surendra Singh Negi; Ramakrishna Ramaswamy
2001-01-01
We show that it is possible to devise a large class of skew-product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is non-positive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics is not necessary for the creation of SNAs.
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.
Supersymmetry, attractors and cosmic censorship
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
Asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized. In the case of this system with an inversion symmetry, it is shown that symmetric attractors bounded by genus-one tori are conveniently analyzed using a two-components Poincaré section. Resulting from a merging attractor crisis, these attractors can be easily described as being made of two folding mechanisms (here described as mixers), one for each of the two attractors co-existing before the crisis: symmetric attractors are thus described by a template made of two mixers. We thus developed a procedure for concatenating two mixers (here associated with unimodal maps) into a single one, allowing the description of a reduced template, that is, a template simplified under an isotopy. The so-obtained reduced template is associated with a description of symmetric attractors based on one-component Poincaré section as suggested by the corresponding genus-one bounding torus. It is shown that several reduced templates can be obtained depending on the choice of the retained one-component Poincaré section. (paper)
Black Hole Attractors and Pure Spinors
Energy Technology Data Exchange (ETDEWEB)
Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-02-21
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to {Sigma}f{sub k} = Im(C{Phi}), where {Phi} is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, {Phi} = {Omega} and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.
Strange attractor simulated on a quantum computer
Terraneo, M; Shepelyansky, D L
2003-01-01
Starting from the work of Lorenz, it has been realized that the dynamics of many various dissipative systems converges to so-called strange attractors. These objects are characterized by fractal dimensions and chaotic unstable dynamics of individual trajectories. They appear in nature in very different contexts, including applications to turbulence and weather forecast, molecular dynamics, chaotic chemical reactions, multimode solid state lasers and complex dynamics in ecological systems and physiology. The efficient numerical simulation of such dissipative systems can therefore lead to many important practical applications. Here we study a simple deterministic model where dynamics converges to a strange attractor, and show that it can be efficiently simulated on a quantum computer. Even if the dynamics on the attractor is unstable, dissipative and irreversible, a realistic quantum computer can simulate it in a reversible way, and, already with 70 qubits, will provide access to new informations unaccessible f...
Chaotic attractors of two-dimensional invertible maps
Directory of Open Access Journals (Sweden)
Andrey S. Kopeikin
1997-01-01
Full Text Available In this paper, we investigate the characteristics of quasihyperbolic attractors and quasiattractors in Invertible dissipative maps of the plane. The criteria which allow one to diagnose the indicated types of attractors in numerical experiments are formulated.
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
Non-Supersymmetric Attractors in String Theory and Gauged Supergravity
International Nuclear Information System (INIS)
In this article we briefly review the attractor mechanism in the context of N=2 supergravity theories arising from the compactification of type-IIA string theory on a Calabi-Yau manifold. We find non-supersymmetric attractors and discuss their stability. We further discuss the generalization of the attractor mechanism to N=2 gauged supergravity and explicitly construct configurations corresponding to Bianchi attractors
Noise-enhanced reconstruction of attractors
Castro, R G
1997-01-01
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike train prediction error, can be increased by adding noise to the spike creation process. This phenomenon for chaotic systems is an analogue of stochastic resonance.
Attractor merging crisis in chaotic business cycles
International Nuclear Information System (INIS)
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
Pattern recognition using asymmetric attractor neural networks
Jin, Tao; Zhao, Hong
2005-12-01
The asymmetric attractor neural networks designed by the Monte Carlo- (MC-) adaptation rule are shown to be promising candidates for pattern recognition. In such a neural network with relatively low symmetry, when the members of a set of template patterns are stored as fixed-point attractors, their attraction basins are shown to be isolated islands embedded in a “chaotic sea.” The sizes of these islands can be controlled by a single parameter. We show that these properties can be used for effective pattern recognition and rejection. In our method, the pattern to be identified is attracted to a template pattern or a chaotic attractor. If the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold, the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern. Otherwise, it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern. The maximum sizes of these islands allowed by this kind of neural networks are determined by a modified MC-adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands. We illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of Chinese characters.
Pattern recognition using asymmetric attractor neural networks
International Nuclear Information System (INIS)
The asymmetric attractor neural networks designed by the Monte Carlo- (MC-) adaptation rule are shown to be promising candidates for pattern recognition. In such a neural network with relatively low symmetry, when the members of a set of template patterns are stored as fixed-point attractors, their attraction basins are shown to be isolated islands embedded in a ''chaotic sea.'' The sizes of these islands can be controlled by a single parameter. We show that these properties can be used for effective pattern recognition and rejection. In our method, the pattern to be identified is attracted to a template pattern or a chaotic attractor. If the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold, the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern. Otherwise, it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern. The maximum sizes of these islands allowed by this kind of neural networks are determined by a modified MC-adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands. We illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of Chinese characters
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
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.
Recurrence quantification analysis in Liu's attractor
International Nuclear Information System (INIS)
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
Single-field $\\alpha$-attractors
Linde, Andrei
2015-01-01
I describe a simple class of $\\alpha$-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for $0<\\alpha \\lesssim 1$, providing a good match to the present cosmological data. I also present a generalized version of these models which can describe not only inflation but also dark energy and supersymmetry breaking.
Tiling Spaces, Codimension One Attractors and Shape
Clark, Alex
2011-01-01
We show that any codimension one hyperbolic attractor of a di?eomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a ?nite number of points removed, or, in the non-orientable case, to a space with a 2 to 1 covering by such a torus-less-points. Furthermore, we show that each orientable attractor is homeomorphic to a tiling space associated to an aperiodic tiling of Rd, but that the converse is generally not true. This work allows the de?nition of a new invariant for aperiodic tilings, in many cases ?ner than the cohomological or K-theoretic invariants studied to date.
Evidence for attractors in English intonation.
Braun, Bettina; Kochanski, Greg; Grabe, Esther; Rosner, Burton S
2006-06-01
Although the pitch of the human voice is continuously variable, some linguists contend that intonation in speech is restricted to a small, limited set of patterns. This claim is tested by asking subjects to mimic a block of 100 randomly generated intonation contours and then to imitate themselves in several successive sessions. The produced f0 contours gradually converge towards a limited set of distinct, previously recognized basic English intonation patterns. These patterns are "attractors" in the space of possible intonation English contours. The convergence does not occur immediately. Seven of the ten participants show continued convergence toward their attractors after the first iteration. Subjects retain and use information beyond phonological contrasts, suggesting that intonational phonology is not a complete description of their mental representation of intonation. PMID:16838543
Sneutrino Inflation with $\\alpha$-attractors
Kallosh, Renata; Roest, Diederik; Wrase, Timm
2016-01-01
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.
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.
Cortical attractor network dynamics with diluted connectivity.
Rolls, Edmund T; Webb, Tristan J
2012-01-24
The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding". PMID:21875702
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: 0.477, year: 2014 http://www.apcz.pl/czasopisma/index.php/TMNA/article/view/TMNA.2015.076
Attractor Solutions in f(T) Cosmology
Jamil, Mubasher; Momeni, D.; Myrzakulov, Ratbay
2012-01-01
In this paper, we explore the cosmological implications of interacting dark energy model in a torsion based gravity namely $f(T)$. Assuming dark energy interacts with dark matter and radiation components, we examine the stability of this model by choosing different forms of interaction terms. We consider three different forms of dark energy: cosmological constant, quintessence and phantom energy. We then obtain several attractor solutions for each dark energy model interacting with other comp...
Lipschitz deviation and embeddings of global attractors
International Nuclear Information System (INIS)
Hunt and Kaloshin (1999 Nonlinearity 12 1263–75) proved that it is possible to embed a compact subset X of a Hilbert space with upper box-counting dimension d N for any N > 2k + 1, using a linear map L whose inverse is Hölder continuous with exponent α N, dH(L(X)) ≥ min(N, dH(X)/(1 + τ(X)/2)). They also conjectured that 'many of the attractors associated with the evolution equations of mathematical physics have thickness exponent zero'. In this paper we introduce a variant of the thickness exponent, the Lipschitz deviation dev(X): we show that in both of the above results this can be used in place of the thickness exponent, and—appealing to results from the theory of approximate inertial manifolds—we prove that dev(X) = 0 for the attractors of a wide class of semilinear parabolic equations, thus providing a partial answer to the conjecture of Ott, Hunt and Kaloshin. In particular, dev(X) = 0 for the attractor of the 2D Navier–Stokes equations with forcing f in L2, while current results only guarantee that τ(X) = 0, when f in C∞
Inflationary quasi-scale invariant attractors
Rinaldi, Massimiliano; Zerbini, Sergio; Venturi, Giovanni
2016-01-01
In a series of papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $\\alpha$. These so-called $\\alpha$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $\\alpha$-attractors is the analyticity of the scalar potential in the non-canonical Einstein frame. In this paper we explore the case of non-analytic potentials and we find that they lead to a class of attractors characterized by quasi-scale invariance in the Jordan frame. In the canonical Einstein frame they all converge to a model with a linear potential and a universal relation between $r$ and $n_{s}$ that can fit the observational data. We show that the breaking of exact, classical, scale invariance in the Jordan frame can be attributed to one-loop corrections, in line with previous results...
Attractors for the penalized Navier-Stokes equations
International Nuclear Information System (INIS)
Consideration is given to the penalized form of the Navier-Stokes equations for a viscous incompressible fluid where the pressure and the incompressibility equations are suppressed and replaced by a penalty term in the momentum conservation equation. Here, the existence of an attractor for the penalized Navier-Stokes equation is studied, this attractor describing the long-time behavior of the solutions. Then the penalty parameter is allowed to tend to zero, and it is shown how the attractors of the penalized equations approximate the attractor of the exact equations. 19 references
METHODOLOGICAL NOTES: Strange attractors in rattleback dynamics
Borisov, Aleksei V.; Mamaev, Ivan S.
2003-04-01
This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters.
Attractor Explosions and Catalyzed Vacuum Decay
Energy Technology Data Exchange (ETDEWEB)
Green, Daniel; Silverstein, Eva; Starr, David
2006-05-05
We present a mechanism for catalyzed vacuum bubble production obtained by combining moduli stabilization with a generalized attractor phenomenon in which moduli are sourced by compact objects. This leads straightforwardly to a class of examples in which the Hawking decay process for black holes unveils a bubble of a different vacuum from the ambient one, generalizing the new endpoint for Hawking evaporation discovered recently by Horowitz. Catalyzed vacuum bubble production can occur for both charged and uncharged bodies, including Schwarzschild black holes for which massive particles produced in the Hawking process can trigger vacuum decay. We briefly discuss applications of this process to the population and stability of metastable vacua.
Energy cascade in internal wave attractors
Brouzet, Christophe; Joubaud, Sylvain; Sibgatullin, Ilias; Dauxois, Thierry
2016-01-01
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction.
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.
Pointed shape and global attractors for metrizable spaces A
Romero Ruiz del Portal, Francisco; Giraldo, A.; Jimenez, R; Morón, Manuel A.; Rodríguez Sanjurjo, José Manuel
2011-01-01
In this paper we consider two notions of attractors for semidynamical systems de ned in metric spaces. We show that Borsuk's weak and strong shape theories are a convenient framework to study the global properties which the attractor inherits from the phase space. Moreover we obtain pointed equivalences (even in the absence of equilibria) which allow to consider also pointed invariants, like shape groups.
Random attractor of non-autonomous stochastic Boussinesq lattice system
Energy Technology Data Exchange (ETDEWEB)
Zhao, Min, E-mail: zhaomin1223@126.com; Zhou, Shengfan, E-mail: zhoushengfan@yahoo.com [Department of Mathematics, Zhejiang Normal University, Jinhua 321004 (China)
2015-09-15
In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.
Experimental confirmation of a new reversed butterfly-shaped attractor
Institute of Scientific and Technical Information of China (English)
Liu Ling; Su Yan-Chen; Liu Chong-Xin
2007-01-01
This paper reports a new reverse butterfly-shaped chaotic attractor and its experimental confirmation. Some basic dynamical properties, and chaotic behaviours of this new reverse butterfly attractor are studied. Simulation results support brief theoretical derivations. Furthermore, the system is experimentally confirmed by a simple electronic circuit.
Random attractor of non-autonomous stochastic Boussinesq lattice system
International Nuclear Information System (INIS)
In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero
Finite fractal dimensionality of attractors for nonlocal evolution equations
Directory of Open Access Journals (Sweden)
Severino Horacio da Silva
2013-09-01
Full Text Available In this work we consider the Dirichlet problem governed by a non local evolution equation. We prove the existence of exponential attractors for the flow generated by this problem, and as a consequence we obtain the finite dimensionality of the global attractor whose existence was proved in [1
Cosmological attractors and initial conditions for inflation
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei
2015-09-01
Inflationary α -attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincaré disk hyperbolic geometry. We refine these models by constructing Kähler potentials with built-in inflaton shift symmetry and by making a canonical choice of the Goldstino Kähler potential. The refined models are stable with respect to all scalar fields at all α ; no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field φ and an infinitely long de Sitter (dS) valley of constant depth and width at large φ . Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field φ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large φ . This provides natural initial conditions for inflation driven by the inflaton field slowly rolling along the dS valley toward the minimum of the potential at small φ . A detailed description of this process is given for α -attractors in supergravity, but we believe that our general conclusions concerning naturalness of initial conditions for inflation are valid for a broad class of inflationary models with sufficiently flat potentials.
Strange Attractor in Immunology of Tumor Growth
Voitikova, M
1997-01-01
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation parameter. Increase in the growth rate results in instability of the tumor state and causes period-doubling bifurcations in the immune+tumor system. For larger values of tumor growth rate a strange attractor has been observed. The model proposed is able to describe the metastable-state production when time series data of the immune state and the number of tumor cells are irregular and unpredictable. This metastatic disease may be caused not by exterior (medical) factors, but interior density dependent ones.
A Chaotic Attractor in Delayed Memristive System
Directory of Open Access Journals (Sweden)
Lidan Wang
2012-01-01
Full Text Available Over the last three decades, theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science. In 2008, the successful development of memristor brings new activity for this research. Memristor is a new nanometre-scale passive circuit element, which possesses memory and nonlinear characteristics. This makes it have a unique charm to attract many researchers’ interests. In this paper, memristor, for the first time, is introduced in a delayed system to design a signal generator to produce chaotic behaviour. By replacing the nonlinear function with memristors in parallel, the memristor oscillator exhibits a chaotic attractor. The simulated results demonstrate that the performance is well predicted by the mathematical analysis and supports the viability of the design.
Time Series Prediction Based on Chaotic Attractor
Institute of Scientific and Technical Information of China (English)
LIKe-Ping; CHENTian-Lun; GAOZi-You
2003-01-01
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.
Non-linear fate of internal wave attractors
Scolan, Hélène; Dauxois, Thierry
2013-01-01
We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing.
No fermionic wigs for BPS attractors in 5 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gentile, Lorenzo G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, I-35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova (Italy); Grassi, Pietro A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); INFN – Gruppo Collegato di Alessandria – Sezione di Torino (Italy); Marrani, Alessio, E-mail: alessio.marrani@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Mezzalira, Andrea, E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique, Université Libre de Bruxelles, C.P. 231, B-1050 Bruxelles (Belgium); Sabra, Wafic A., E-mail: ws00@aub.edu.lb [Centre for Advanced Mathematical Sciences and Physics Department, American University of Beirut (Lebanon)
2014-07-30
We analyze the fermionic wigging of 1/2-BPS (electric) extremal black hole attractors in N=2, D=5 ungauged Maxwell–Einstein supergravity theories, by exploiting anti-Killing spinors supersymmetry transformations. Regardless of the specific data of the real special geometry of the manifold defining the scalars of the vector multiplets, and differently from the D=4 case, we find that there are no corrections for the near-horizon attractor value of the scalar fields; an analogous result also holds for 1/2-BPS (magnetic) extremal black string. Thus, the attractor mechanism receives no fermionic corrections in D=5 (at least in the BPS sector)
CMB and reheating constraints to \\alpha-attractor inflationary models
Eshaghi, Mehdi; Riazi, Nematollah; Kiasatpour, Ahmad
2016-01-01
After Planck 2013, a broad class of inflationary models called \\alpha-attractors was developed which has universal observational predictions. For small values of the parameter \\alpha, the models have good consistency with the recent CMB data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, n_s and tensor-to-scalar ratio, r and then using BICEP2/Keck 2015 data we impose constraints on \\alpha-attractors. Then, we study the reheating in \\alpha-attractors. The reheating temperature, T_{re} and the number of e-folds during reheating, N_{re} are calculated as functions of n_s. Using these results, we determine the range of free parameter \\alpha for two clasees of \\alpha-attractors which satisfy the constraints of recent CMB data.
Features from the non-attractor beginning of inflation
Cai, Yi-Fu; Wang, Dong-Gang; Wang, Ziwei
2016-01-01
We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several $e$-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Guassianity due to the "from non-attractor to slow-roll" transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initial non-attractor phase yields interesting features in both power spectrum and bispectrum.
The attractor of the stochastic generalized Ginzburg-Landau equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H01.
Investigating the Rossler Attractor Using Lorentz Plot and Lyapunov Exponents
P. Kvarda
2002-01-01
To investigate the Rossler attractor, introduced in 1976 by O.E. Rossler [3], we used Lorenz plot to show deterministic character and designated the Lyapunov exponent to show the chaotic character of the system.
Algorithms for Finding Small Attractors in Boolean Networks
Directory of Open Access Journals (Sweden)
Hayashida Morihiro
2007-01-01
Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.
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...
Non-supersymmetric attractors in R2 gravities
International Nuclear Information System (INIS)
We investigate the attractor mechanism for spherically symmetric extremal black holes in a theory of general R2 gravity in 4-dimensions, coupled to gauge fields and moduli fields. For the general R2 theory, we look for solutions which are analytic near the horizon, show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of an effective potential at the horizon. This analysis includes the backreaction and supports the validity of non-supersymmetric attractors in the presence of higher derivative interactions. To include a wider class of solutions, we continue our analysis for the specific case of a Gauss-Bonnet theory which is non- topological, due to the coupling of Gauss-Bonnet terms to the moduli fields. We find that the regularity of moduli fields at the horizon is sufficient for attractor behavior. For the non-analytic sector, this regularity condition in turns implies the minimality of the effective potential at the attractor point. (author)
Cosmological Attractors and Initial Conditions for Inflation
Carrasco, John Joseph M; Linde, Andrei
2015-01-01
Inflationary $\\alpha$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $\\alpha$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $\\varphi$, and an infinitely long dS valley of constant depth and width at large $\\varphi$. Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field $\\varphi$ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large $\\varphi$. This provides natural initial conditions for inflation driv...
Strange Attractors Characterizing the Osmotic Instability
Tzenov, Stephan I
2014-01-01
In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic equations describing the process of forward osmosis have been obtained. It has been shown that these equations are very similar to the ones used to model the free Rayleigh-Benard convection. The difference is that while in the case of thermal convection the volume expansion is driven by the coefficient of thermal expansion, the key role for the osmotic instability is played by the coefficient of isothermal compressibility. In addition, it has been shown that the osmotic process represents a propagation of standing waves with time-dependent amplitudes and phase velocity, which equals the current velocity of the solvent passing through the semi-permeable membrane. The evolution of the amplitudes of the osmotic waves is exactly following the dynamics of a strange attractor of Loren...
Structures in the Great Attractor Region
Radburn-Smith, D J; Woudt, P A; Kraan-Korteweg, R C; Watson, F G
2006-01-01
To further our understanding of the Great Attractor (GA), we have undertaken a redshift survey using the 2dF on the AAT. Clusters and filaments in the GA region were targeted with 25 separate pointings resulting in approximately 2600 new redshifts. Targets included poorly studied X-ray clusters from the CIZA catalogue as well as the Cen-Crux and PKS 1343-601 clusters, both of which lie close to the classic GA centre. For nine clusters in the region, we report velocity distributions as well as virial and projected mass estimates. The virial mass of CIZA J1324.7-5736, now identified as a separate structure from the Cen-Crux cluster, is found to be ~3x10^14 M_sun, in good agreement with the X-ray inferred mass. In the PKS 1343-601 field, five redshifts are measured of which four are new. An analysis of redshifts from this survey, in combination with those from the literature, reveals the dominant structure in the GA region to be a large filament, which appears to extend from Abell S0639 (l=281\\deg, b=+11\\deg) to...
Nonnuclear Attractors in Heteronuclear Diatomic Systems.
Terrabuio, Luiz Alberto; Teodoro, Tiago Quevedo; Matta, Chérif F; Haiduke, Roberto Luiz Andrade
2016-03-01
Nonnuclear attractors (NNAs) are observed in the electron density of a variety of systems, but the factors governing their appearance and their contribution to the system's properties remain a mystery. The NNA occurring in homo- and heteronuclear diatomics of main group elements with atomic numbers up to Z = 38 is investigated computationally (at the UCCSD/cc-pVQZ level of theory) by varying internuclear separations. This was done to determine the NNA occurrence window along with the evolution of the respective pseudoatomic basin properties. Two distinct categories of NNAs were detected in the data analyzed by means of catastrophe theory. Type "a" implies electronic charge transfer between atoms mediated by a pseudoatom. Type "b" shows an initial relocation of some electronic charge to a pseudoatom, which posteriorly returns to the same atom that donated this charge in the first place. A small difference of polarizability between the atoms that compose these heteronuclear diatomics seems to favor NNA formation. We also show that the NNA arising tends to result in some perceptible effects on molecular dipole and/or quadrupole moment curves against internuclear distance. Finally, successive cationic ionization results in the fast disappearance of the NNA in Li2 indicating that its formation is mainly governed by the field generated by the quantum mechanical electronic density and only depends parametrically on the bare nuclear field/potential at a given molecular geometry. PMID:26842391
Attractors and soak times in artisanal fi shing with traps
Directory of Open Access Journals (Sweden)
Evandro Figueiredo Sebastiani
2009-12-01
Full Text Available Traps are used by artisanal fishers as fishing gear in places where other fishing modalities are impeded or limited. The advantage of this type of fishing modality is the possibility of keeping fish alive and in the case of capturing species of low commercial value or size below the permitted minimum this fishing gear allows the release of such specimens back to nature, resulting in a sustainability aspect to the use of this fishing gear. This study aims to evaluate the effects of different attractors and times of submersion on the efficiency of the traps used. Sardines, shrimps and trash fish were employed as attractors. To evaluate the soak time, two periods were tested: 24 and 96 hours. The sardines, used as the attractor, resulted in a production of 1,296.4 ± 397.4g, significantly superior (p <0.05 to other attractors. In relation to the soak time, the period of 24 hours resulted in an average production of 1,719.2 ± 866.0g, significantly (p <0.05 superior to the period of 96 hours. The results led to the conclusion that to optimize this capture by fishing gear, sardines should be used as the attractor, together with a soak time of 24 hours.
Attractors of equations of non-Newtonian fluid dynamics
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Li Chunguang [Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: cgli@uestc.edu.cn; Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong (China)]. E-mail: gchen@ee.cityu.edu.hk
2005-03-01
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.
A new butterfly-shaped attractor of Lorenz-like system
International Nuclear Information System (INIS)
In this letter a new butterfly-shaped chaotic attractor is reported. Some basic dynamical properties, such as Poincare mapping, Lyapunov exponents, fractal dimension, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied. Furthermore, we clarify that the chaotic attractors of the system is a compound structure obtained by merging together two simple attractors through a mirror operation
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: 0.918, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mma.3526/abstract
Uniform attractors of non-autonomous dissipative semilinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The asymptotic long time behaviors of a certain type of non-autonomous dissipative semilinear wave equations are studied. The existence of uniform attractors is proved and their upper bounds for both Hausdorff and Fractal dimensions of uniform are given when the external force satisfies suitable conditions.
Global Periodic Attractor for Strongly Damped and Driven Wave Equations
Institute of Scientific and Technical Information of China (English)
Hong-yan Li; Sheng-fan Zhou
2006-01-01
In this paper we consider the strongly damped and driven nonlinear wave equations under homogeneous Dirichlet boundary conditions. By introducing a new norm which is equivalent to the usual norm, we obtain the existence of a global periodic attractor attracting any bounded set exponentially in the phase space,which implies that the system behaves exactly as a one-dimensional system.
A non-reward attractor theory of depression.
Rolls, Edmund T
2016-09-01
A non-reward attractor theory of depression is proposed based on the operation of the lateral orbitofrontal cortex and supracallosal cingulate cortex. The orbitofrontal cortex contains error neurons that respond to non-reward for many seconds in an attractor state that maintains a memory of the non-reward. The human lateral orbitofrontal cortex is activated by non-reward during reward reversal, and by a signal to stop a response that is now incorrect. Damage to the human orbitofrontal cortex impairs reward reversal learning. Not receiving reward can produce depression. The theory proposed is that in depression, this lateral orbitofrontal cortex non-reward system is more easily triggered, and maintains its attractor-related firing for longer. This triggers negative cognitive states, which in turn have positive feedback top-down effects on the orbitofrontal cortex non-reward system. Treatments for depression, including ketamine, may act in part by quashing this attractor. The mania of bipolar disorder is hypothesized to be associated with oversensitivity and overactivity in the reciprocally related reward system in the medial orbitofrontal cortex and pregenual cingulate cortex. PMID:27181908
On reliability of singular-value decomposition in attractor reconstruction
International Nuclear Information System (INIS)
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
GLOBAL ATTRACTOR OF NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E1 space is obtained.
EXPONENTIAL ATTRACTOR FOR A CLASS OF NONCLASSICAL DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
尚亚东; 郭柏灵
2003-01-01
In this paper,we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation.We show the squeezing property and the existence of exponential attractor for this equation.We also make the estimates on its fractal dimension and exponential attraction.
Spatial asymmetric retrieval states in binary attractor neural network
International Nuclear Information System (INIS)
In this paper we show that during the retrieval process in a binary Hebb attractor neural network, spatial localized states can be observed when the connectivity of the network is distance-dependent and there is an asymmetry between the retrieval and the learning states
Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach
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
An attractor for the dynamical state of the intracluster medium
Juncher, Diana; Macciò, Andrea V
2012-01-01
Galaxy clusters provide us with important information about the cosmology of our universe. Observations of the X-ray radiation or of the SZ effect allow us to measure the density and temperature of the hot intergalactic medium between the galaxies in a cluster, which then allow us to calculate the total mass of the galaxy cluster. However, no simple connection between the density and the temperature profiles has been identified. Here we use controlled high-resolution numerical simulations to identify a relation between the density and temperature of the gas in equilibrated galaxy clusters. We demonstrate that the temperature-density relation is a real attractor, by showing that a wide range of equilibrated structures all move towards the attractor when perturbed and subsequently allowed to relax. For structures which have undergone sufficient perturbations for this connection to hold, one can therefore extract the mass profile directly from the X-ray intensity profile.
Non-Abelian magnetized blackholes and unstable attractors
International Nuclear Information System (INIS)
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 AdS2 x S2, 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)
A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension
Munmuangsaen, Buncha; Sprott, Julien Clinton; Thio, Wesley Joo-Chen; Buscarino, Arturo; Fortuna, Luigi
This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from 2.0 to 3.0 by a single control parameter. Such a parameter provides a means to explore the route through limit cycles, period-doubling, dissipative chaos, and eventually conservative chaos. With an absolute-value nonlinearity and certain choices of parameters, the systems have a vast and smooth continual transition path from dissipative chaos to conservative chaos. One system is analyzed in detail by means of the largest Lyapunov exponent, Kaplan-Yorke dimension, bifurcations, coexisting attractors and eigenvalues of the Jacobian matrix. An electronic version of the system has been constructed and shown to perform in accordance with expectations.
Torus-doubling process via strange nonchaotic attractors
International Nuclear Information System (INIS)
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.
Explosion of strange attractors exhibited by Duffing's equation
International Nuclear Information System (INIS)
Recently chaotic behavior in deterministic systems attracts attention of researchers in various fields. By using analog and digital computers, the author has long been engaged himself in the investigation on this kind of motion exhibited by Duffing's equation and has called the phenomenon the chaotically transitional process. The chaotically transitional process is attributed to both the small uncertain factors in the physical system and the global structure of the solutions of the equation. This paper also deals with chaotically transitional processes exhibited by Duffing's equation. The results obtained in the series of our reports and the unsolved problems developed from them are summarized. Special attention is directed towards the transition of the processes under the variation of the system parameter. The explosion of the strange attractor, i.e., an interesting type of transition from strange to strange attractor has been made clear. (author)
Lifetime of chaotic attractors in a multidimensional laser system
International Nuclear Information System (INIS)
We study the lifetimes of chaotic attractors at crises in a multidimensional laser system. This system describes the CO2 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
General relativity as an attractor for scalar-torsion cosmology
Järv, Laur; Toporensky, Alexey
2016-01-01
We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal in this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity (GR). These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism for how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.
Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization
Santos, Augusto Almeida; Krishnan, Ramayya; Moura, José M F
2016-01-01
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits \\emph{good} convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.
Reconstruction of the El Nino attractor with neural networks
International Nuclear Information System (INIS)
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.)
Čech cohomology of attractors of discrete dynamical systems
Ruiz del Portal, Francisco R.; Sánchez-Gabites, J. J.
2014-10-01
Let f:Rn→Rn be a homeomorphism and K an asymptotically stable attractor for f. The aim of this paper is to study when the inclusion of K in its basin of attraction A(K) induces isomorphisms in Čech cohomology. We show that (i) this is true if coefficients are taken in Q or Zp (p prime) and (ii) it is true for integral cohomology if and only if the Čech cohomology of K or A(K) is finitely generated. We compute the Čech cohomology of periodic point free attractors of volume-contracting R3-homeomorphisms and present applications to quite general models in population dynamics.
Measurement of cardiovascular state using attractor reconstruction analysis
Charlton, Peter Harcourt; Camporota, Luigi; Smith, John; Nandi, Manasi; Christie, Mark Ian; Aston, Philip; Beale, Richard
2015-01-01
Attractor reconstruction (AR) analysis has been used previously to quantify the variability in arterial blood pressure (ABP) signals. Since ABP signals are only available in a minority of clinical scenarios, we sought to determine whether AR could also be performed on more widely available photoplethysmogram (PPG) signals. AR analysis was performed on simultaneous ABP and PPG signals before, during and after a change in cardiovascular state. A novel quality metric was used to eliminate window...
Attractors and chaos of electron dynamics in electromagnetic standing wave
Esirkepov, Timur Zh; Koga, James K; Kando, Masaki; Kondo, Kiminori; Rosanov, Nikolay N; Korn, Georg; Bulanov, Sergei V
2014-01-01
The radiation reaction radically influences the electron motion in an electromagnetic standing wave formed by two super-intense counter-propagating laser pulses. Depending on the laser intensity and wavelength, either classical or quantum mode of radiation reaction prevail, or both are strong. When radiation reaction dominates, electron motion evolves to limit cycles and strange attractors. This creates a new framework for high energy physics experiments on an interaction of energetic charged particle beams and colliding super-intense laser pulses.
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)
Labyrinthine pathways towards supercycle attractors in unimodal maps
Moyano, Luis; Silva, D.; Robledo, A.
2009-09-01
As an important preceding step for the demonstration of an uncharacteristic (q-deformed) statisticalmechanical structure in the dynamics of the Feigenbaum attractor we uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the pre-images of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated with the family of supercycles. iv) This map is given in closed form by the same kind of q-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is final-stage ultra-fast dynamics towards the attractor, with a sensitivity to initial conditions which decreases as an exponential of an exponential of time. We discuss the relevance of these properties to the comprehension of the discrete scale-invariance features, and to the identification of the statistical-mechanical framework present at the period-doubling transition to chaos. This is the first of three studies (the other two are quoted in the text) which together lead to a definite conclusion about the applicability of q-statistics to the dynamics associated to the Feigenbaum attractor.
Pattern Selection in Network of Coupled Multi-Scroll Attractors.
Li, Fan; Ma, Jun
2016-01-01
Multi-scroll chaotic attractor makes the oscillator become more complex in dynamic behaviors. The collective behaviors of coupled oscillators with multi-scroll attractors are investigated in the regular network in two-dimensional array, which the local kinetics is described by an improved Chua circuit. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns. Firstly, the Chua circuit is improved by replacing the nonlinear term with Sine function to generate infinite aquariums so that multi-scroll chaotic attractors could be generated under appropriate parameters, which could be detected by calculating the Lyapunov exponent in the parameter region. Furthermore, negative feedback with different gains (D1, D2) is imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gain with diversity and size of controlled area. Particularly, homogeneous state could be reached after synchronization by selecting appropriate feedback gain and controlled size in the network. Finally, the distribution for statistical factors of synchronization is calculated in the two-parameter space to understand the transition of pattern region. It is found that developed spiral waves, target waves often are associated with smaller factor of synchronization. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely. PMID:27119986
Effective field theory of non-attractor inflation
Energy Technology Data Exchange (ETDEWEB)
Akhshik, Mohammad [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Jazayeri, Sadra [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of)
2015-07-29
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
Unstable periodic orbits and attractor of the barotropic ocean model
Directory of Open Access Journals (Sweden)
E. Kazantsev
1998-01-01
Full Text Available A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its implementation for geophysical models. This method was used to find numerically several low-period orbits for the barotropic ocean model in a square. Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF of principal parameters. These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation. The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
Entropies from Markov Models as Complexity Measures of Embedded Attractors
Directory of Open Access Journals (Sweden)
Julián D. Arias-Londoño
2015-06-01
Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.
Required criteria for recognizing new types of chaos: application to the "cord" attractor.
Letellier, Christophe; Aguirre, Luis A
2012-03-01
After suggesting criteria to recognize a new system and a new attractor-and to make a distinction between them-the paper details the topological analysis of the "cord" attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation [L. A. Aguirre and C. Letellier, Phys. Rev. E 83, 066209 (2011)]. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global π twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics. PMID:22587158
Noise-induced attractor annihilation in the delayed feedback logistic map
International Nuclear Information System (INIS)
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.
Noise-induced attractor annihilation in the delayed feedback logistic map
Energy Technology Data Exchange (ETDEWEB)
Pisarchik, A.N., E-mail: apisarch@cio.mx [Centro de Investigaciones en Optica, Loma del Bosque 115, Leon, Guanajuato (Mexico); Centre for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid (Spain); Martínez-Zérega, B.E. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon 1144, Paseos de la Montaña, Lagos de Moreno, Jalisco 47460 (Mexico)
2013-12-06
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.
On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
Ferrara, Sergio
2007-01-01
We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d=5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kahler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N=2, d=5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.
Application of fixed point theory to chaotic attractors of forced oscillators
International Nuclear Information System (INIS)
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)
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.
Neural attractor network for application in visual field data classification
International Nuclear Information System (INIS)
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
Neural attractor network for application in visual field data classification
Fink, Wolfgang
2004-07-01
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.
Neural attractor network for application in visual field data classification
Energy Technology Data Exchange (ETDEWEB)
Fink, Wolfgang [Doheny Eye Institute, Keck School of Medicine at the University of Southern California, Los Angeles, CA 90033 (United States); California Institute of Technology, Pasadena, CA 91125 (United States)
2004-07-07
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
Analysis of stochastically forced quasi-periodic attractors
Energy Technology Data Exchange (ETDEWEB)
Ryashko, Lev [Ural Federal University, Lenina, 51, Ekaterinburg, 620000 (Russian Federation)
2015-11-30
A problem of the analysis of stochastically forced quasi-periodic auto-oscillations of nonlinear dynamic systems is considered. A stationary distribution of random trajectories in the neighborhood of the corresponding deterministic attractor (torus) is studied. A parametric description of quadratic approximation of the quasipotential based on the stochastic sensitivity functions (SSF) technique is given. Using this technique, we analyse a dispersion of stochastic flows near the torus. For the case of two-torus in three-dimensional space, the stochastic sensitivity function is constructed.
Analysis of stochastically forced quasi-periodic attractors
International Nuclear Information System (INIS)
A problem of the analysis of stochastically forced quasi-periodic auto-oscillations of nonlinear dynamic systems is considered. A stationary distribution of random trajectories in the neighborhood of the corresponding deterministic attractor (torus) is studied. A parametric description of quadratic approximation of the quasipotential based on the stochastic sensitivity functions (SSF) technique is given. Using this technique, we analyse a dispersion of stochastic flows near the torus. For the case of two-torus in three-dimensional space, the stochastic sensitivity function is constructed
Generalized Pole Inflation: Hilltop, Natural, and Chaotic Inflationary Attractors
Terada, Takahiro
2016-01-01
A new paradigm for inflationary model building 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, or monomial or polynomial chaotic inflation. We demonstrate attractor behavior of these models and compute corrections from the additional poles to the inflationary observables.
Exploring strange nonchaotic attractors through Jacobian elliptic functions
International Nuclear Information System (INIS)
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of quasiperiodically forced systems. We found similar scenarios of SNAs from the analysis of two representative examples: a quasiperiodically forced damped pendulum and a two-dimensional map. This clearly well-suited and advantageous use of the JEFs, which in their own right lie at the heart of nonlinear physics, may encourage students at intermediate university levels to study them in depth.
Chaotic attractor transforming control of hybrid Lorenz-Chen system
Institute of Scientific and Technical Information of China (English)
Qi Dong-Lian; Wang Qiao; Gu Hong
2008-01-01
Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization.According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten.The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.
Exploring strange nonchaotic attractors through Jacobian elliptic functions
Energy Technology Data Exchange (ETDEWEB)
GarcIa-Hoz, A Martinez [Departamento de Fisica Aplicada, Escuela Universitaria Politecnica, Universidad de Castilla La Mancha, E-13400 Almaden (Ciudad Real) (Spain); Chacon, R, E-mail: rchacon@unex.es [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz (Spain)
2011-11-15
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of quasiperiodically forced systems. We found similar scenarios of SNAs from the analysis of two representative examples: a quasiperiodically forced damped pendulum and a two-dimensional map. This clearly well-suited and advantageous use of the JEFs, which in their own right lie at the heart of nonlinear physics, may encourage students at intermediate university levels to study them in depth.
The asymptotic number of attractors in the random map model
International Nuclear Information System (INIS)
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as its image. We derive here explicit formulae for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulae increases exponentially with n; therefore, they are not directly applicable to study the behaviour of systems where n is large. However, our formulae can be used to derive useful asymptotic expressions, as we show
A novel strange attractor and its dynamic analysis
Directory of Open Access Journals (Sweden)
Zhongtang Wu
2014-03-01
Full Text Available In this paper, not only a novel three-dimensional autonomous strange attractor is proposed, but also an idea to generate a more complex chaotic system was introduced. Of particular interest is that this novel system has complex phase diagram, big positive Lyapunov exponent and broad frequency spectrum. With either analytical or numerical methods, basic properties of the system, such as dynamical behaviors (time history and phase diagrams, Poincáre mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The obtained results clearly show that this is a new chaotic system which has good application prospects.
Experimental exploration of the optomechanical attractor diagram and its dynamics
Buters, Frank M; Heeck, Kier; Weaver, Matthew J; Pepper, Brian; de Man, Sven; Bouwmeester, Dirk
2015-01-01
We demonstrate experimental exploration of the attractor diagram of an optomechanical system where the optical forces compensate for the mechanical losses. In this case stable self-induced oscillations occur but only for specific mirror amplitudes and laser detunings. We demonstrate that we can amplify the mechanical mode to an amplitude 500 times larger than the thermal amplitude at 300K. The lack of unstable or chaotic motion allows us to manipulate our system into a non-trivial steady state and explore the dynamics of self-induced oscillations in great detail.
The hot attractor mechanism: decoupling without deep throats
Goldstein, Kevin; Jejjala, Vishnu; Nampuri, Suresh
2016-01-01
Non-extremal black holes in N = 2 $$ \\mathcal{N}=2 $$ supergravity have two horizons, the geometric mean of whose areas recovers the horizon area of the extremal black hole obtained from taking a smooth zero temperature limit. In prior work [1] using the attractor mechanism, we deduced the existence of several moduli independent invariant quantities obtained from averaging over a decoupled inter-horizon region. We establish that non-extremal geometries at the Reissner-Nordström point, where t...
Attractors and chaos of electron dynamics in electromagnetic standing waves
International Nuclear Information System (INIS)
In an electromagnetic standing wave formed by two super-intense colliding laser pulses, radiation reaction totally modifies the electron motion. The quantum corrections to the electron motion and the radiation reaction force can be independently small or large, depending on the laser intensity and wavelength, thus dividing the parameter space into 4 domains. The electron motion evolves to limit cycles and strange attractors when radiation reaction dominates. This creates a new framework for high energy physics experiments on the interaction of energetic charged particle beams and colliding super-intense laser pulses
The attractor dimension of solar decimetric radio pulsations
Kurths, J.; Benz, A. O.; Aschwanden, M. J.
1991-01-01
The temporal characteristics of decimetric pulsations and related radio emissions during solar flares are analyzed using statistical methods recently developed for nonlinear dynamic systems. The results of the analysis is consistent with earlier reports on low-dimensional attractors of such events and yield a quantitative description of their temporal characteristics and hidden order. The estimated dimensions of typical decimetric pulsations are generally in the range of 3.0 + or - 0.5. Quasi-periodic oscillations and sudden reductions may have dimensions as low as 2. Pulsations of decimetric type IV continua have typically a dimension of about 4.
Attractors and chaos of electron dynamics in electromagnetic standing waves
Energy Technology Data Exchange (ETDEWEB)
Esirkepov, Timur Zh. [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan); Bulanov, Stepan S. [University of California, Berkeley, CA 94720 (United States); Koga, James K.; Kando, Masaki; Kondo, Kiminori [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan); Rosanov, Nikolay N. [Vavilov State Optical Institute, Saint-Petersburg 199034 (Russian Federation); Korn, Georg [ELI Beamline Facility, Institute of Physics, Czech Academy of Sciences, Prague 18221 (Czech Republic); Bulanov, Sergei V., E-mail: bulanov.sergei@jaea.go.jp [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan)
2015-09-25
In an electromagnetic standing wave formed by two super-intense colliding laser pulses, radiation reaction totally modifies the electron motion. The quantum corrections to the electron motion and the radiation reaction force can be independently small or large, depending on the laser intensity and wavelength, thus dividing the parameter space into 4 domains. The electron motion evolves to limit cycles and strange attractors when radiation reaction dominates. This creates a new framework for high energy physics experiments on the interaction of energetic charged particle beams and colliding super-intense laser pulses.
Lorenz-like attractors in a nonholonomic model of a rattleback
Gonchenko, A. S.; Gonchenko, S. V.
2015-09-01
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.
The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation
Institute of Scientific and Technical Information of China (English)
Rui-feng Zhang
2008-01-01
The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.
Attractor scenarios and superluminal signals in k-essence cosmology
Kang, Jin U; Winitzki, Sergei
2007-01-01
Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field \\phi. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)/\\phi^2, necessarily involve an epoch where perturbations of \\phi propagate faster than light (the "no-go theorem"). We carry out a comprehensive study of attractor-like cosmological solutions ("trackers") involving a k-essence scalar field \\phi and another matter component. The result of this study is a complete classification of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K(\\phi)L(X) . Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous "no-go theorem" still holds for...
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error. PMID:26754972
Split attractor flow in N=2 minimally coupled supergravity
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio, E-mail: sergio.ferrara@cern.c [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547 (United States); Marrani, Alessio, E-mail: marrani@lnf.infn.i [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305-4060 (United States); Orazi, Emanuele, E-mail: emanuele.orazi@polito.i [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland)
2011-05-21
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 an 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 least in the n=1 case, is analogous to the BPS one.
Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets
Chimento, Samuele; Petri, Nicolò
2015-01-01
We consider four-dimensional $N=2$ supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic K\\"ahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ort\\'{\\i}n in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential ${\\cal F}=-i\\chi^0\\chi^1$, and the universal hypermultiplet. This solution has a running dilaton, and it interpolates between $\\text{AdS}_2\\times\\text{H}^2$ at the horizon and a hyperscaling-violating type geometry at infinity, conformal to $\\text{AdS}_2\\times\\text{H}^2$. It carries two magnetic charges that are completely fixed in terms of the parameters that appear in the Killing vector used for the gauging. In the second part of the paper, we extend the work of Bellucci et al. on black hole attractors in gauged supergravity to the case where also hypermultiplets are present. The attractors are shown to be governed by an effective potent...
Topological origin of global attractors in gene regulatory networks
Zhang, YunJun; Ouyang, Qi; Geng, Zhi
2015-02-01
Fixed-point attractors with global stability manifest themselves in a number of gene regulatory networks. This property indicates the stability of regulatory networks against small state perturbations and is closely related to other complex dynamics. In this paper, we aim to reveal the core modules in regulatory networks that determine their global attractors and the relationship between these core modules and other motifs. This work has been done via three steps. Firstly, inspired by the signal transmission in the regulation process, we extract the model of chain-like network from regulation networks. We propose a module of "ideal transmission chain (ITC)", which is proved sufficient and necessary (under certain condition) to form a global fixed-point in the context of chain-like network. Secondly, by examining two well-studied regulatory networks (i.e., the cell-cycle regulatory networks of Budding yeast and Fission yeast), we identify the ideal modules in true regulation networks and demonstrate that the modules have a superior contribution to network stability (quantified by the relative size of the biggest attraction basin). Thirdly, in these two regulation networks, we find that the double negative feedback loops, which are the key motifs of forming bistability in regulation, are connected to these core modules with high network stability. These results have shed new light on the connection between the topological feature and the dynamic property of regulatory networks.
Generation and control of multi-scroll chaotic attractors in fractional order systems
International Nuclear Information System (INIS)
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
A novel one equilibrium hyper-chaotic system generated upon Lü attractor
International Nuclear Information System (INIS)
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)
Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''
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
Omnidirectional optical attractor in structured gap-surface plasmon waveguide
Sheng, Chong; Liu, Hui; Zhu, Shining; Genov, Dentcho A.
2016-03-01
An optical attractor based on a simple and easy to fabricate structured metal-dielectric-metal (SMDM) waveguide is proposed. The structured waveguide has a variable thickness in the vicinity of an embedded microsphere and allow for adiabatic nano-focusing of gap-surface plasmon polaritons (GSPPs). We show that the proposed system acts as an omnidirectional absorber across a broad spectral range. The geometrical optics approximation is used to provide a description of the ray trajectories in the system and identify the singularity of the deflection angle at the photon sphere. The analytical theory is validated by full-wave numerical simulations demonstrating adiabatic, deep sub-wavelength focusing of GSPPs and high local field enhancement. The proposed structured waveguide is an ideal candidate for the demonstration of reflection free omnidirectional absorption of GSPP in the optical and infrared frequency ranges.
Navigating cancer network attractors for tumor-specific therapy
DEFF Research Database (Denmark)
Creixell, Pau; Schoof, Erwin; Erler, Janine Terra;
2012-01-01
understanding of the processes by which genetic lesions perturb these networks and lead to disease phenotypes. Network biology will help circumvent fundamental obstacles in cancer treatment, such as drug resistance and metastasis, empowering personalized and tumor-specific cancer therapies.......Cells employ highly dynamic signaling networks to drive biological decision processes. Perturbations to these signaling networks may attract cells to new malignant signaling and phenotypic states, termed cancer network attractors, that result in cancer development. As different cancer cells reach...... these malignant states by accumulating different molecular alterations, uncovering these mechanisms represents a grand challenge in cancer biology. Addressing this challenge will require new systems-based strategies that capture the intrinsic properties of cancer signaling networks and provide deeper...
The Hot Attractor Mechanism: Decoupling Without Deep Throats
Goldstein, Kevin; Nampuri, Suresh
2015-01-01
Non-extremal black holes in $\\mathcal{N}=2$ supergravity have two horizons, the geometric mean of whose areas recovers the horizon area of the extremal black hole obtained from taking a smooth zero temperature limit. In prior work (arxiv:1410.3478), using the attractor mechanism, we deduced the existence of several moduli independent invariant quantities obtained from averaging over a decoupled inter-horizon region. We establish that non-extremal geometries at the Reissner--Nordstr\\"om point, where the scalar moduli are held fixed, can be lifted to solutions in supergravity with a near-horizon $AdS_3\\times S^2$. These solutions have the same entropy and temperature as the original black hole and therefore allow an interpretation of the underlying gravitational degrees of freedom in terms of CFT$_2$. Symmetries of the moduli space enable us to explicate the origin of entropy in the extremal limit.
Non-extremal black holes, harmonic functions and attractor equations
International Nuclear Information System (INIS)
We present a method which allows one to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and non-supersymmetric Einstein-vector-scalar-type theories. The deformation is shown to work in general when the scalar and vector couplings are encoded by a Hesse potential irrespective of whether the theory is supersymmetric or not. While the line element is dressed with an additional harmonic function, the attractor equations for the scalars remain unmodified in suitable coordinates, and the values of the scalar fields on the outer and inner horizon are obtained from their fixed point values by making specific substitutions for the charges. For a subclass of models, which includes the five-dimensional STU model, we find explicit solutions.
Broken Scale Invariance, Alpha-Attractors and Vector Impurity
Akarsu, Ozgur; Kahya, Emre O; Ozdemir, Nese; Ozkan, Mehmet
2016-01-01
We show that if the {\\alpha}-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry severely constrains the {\\alpha}-parameter as 5/6 < {\\alpha} < 1, restricting the inflationary predictions in a very tiny region in the n_s vs r plane that are in great agreement with the latest Planck data. Although the different values of {\\alpha} do not make a tangible difference for n_s and r, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.
How organisms do the right thing: The attractor hypothesis
Emlen, John M.; Freeman, D. Carl; Mills, April; Graham, John H.
1998-09-01
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.
Institute of Scientific and Technical Information of China (English)
Yu Si-Min; Ma Zai-Guang; Qiu Shui-Sheng; Peng Shi-Guo; Lin Qing-Hua
2004-01-01
Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems. A fourth-order circuit, by introducing additional breakpoints in the modified Chua oscillator, is implemented for the study of generation and synchronization of N-scroll chaotic attractors. This confirms the consistency of theoretical calculation, numerical simulation and circuit experiment.Furthermore, we give a refined and extended study of generating and synchronizing N-scroll hyperchaotic attractors in the fourth-order MCK system and report the new theoretical result, which is verified by computer simulations.
Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains
Directory of Open Access Journals (Sweden)
Bixiang Wang
2012-04-01
Full Text Available This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. First we introduce a continuous cocycle for the equations and then prove the existence and uniqueness of tempered random attractors. We also characterize the structures of the random attractors by complete solutions. When deterministic forcing terms are periodic, we show that the tempered random attractors are also periodic. Since the Sobolev embeddings on unbounded domains are not compact, we establish the pullback asymptotic compactness of solutions by Ball's idea of energy equations.
Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay
International Nuclear Information System (INIS)
Stochastically forced regular attractors (equilibria, cycles, closed invariant curves) of the discrete-time nonlinear systems are studied. For the analysis of noisy attractors, a unified approach based on the stochastic sensitivity function technique is suggested and discussed. Potentialities of the elaborated theory are demonstrated in the parametric analysis of the stochastic Ricker model with delay nearby Neimark–Sacker bifurcation. - Highlights: • Stochastically forced regular attractors of the discrete-time nonlinear systems are studied. • Unified approach based on the stochastic sensitivity function technique is suggested. • Potentialities of the elaborated theory are demonstrated. • Parametric analysis of the stochastic Ricker model with delay is given
Systematic Computation of the Least Unstable Periodic Orbits in Chaotic Attractors
Diakonos, F K; Biham, O; Diakonos, Fotis K.; Schmelcher, Peter
1998-01-01
We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a modified dynamical system which has the same set of periodic orbits as the original chaotic system, but with a tuning parameter which is used to stabilize the orbits selectively. This technique is central for calculations using the stability criterion for the truncation of cycle expansions, which provide highly improved convergence of calculations of dynamical averages in generic chaotic attractors. The approach is demonstrated for the Henon attractor.
Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type
Directory of Open Access Journals (Sweden)
F. Yu
2013-02-01
Full Text Available n this paper, a new three-dimension (3D autonomous chaotic system with a nonlinear term in the form of a hyperbolic sine (or cosine function is reported. Some interesting and complex attractors are obtained. Basic dynamical properties of the new chaotic system are demonstrated in terms of Lyapunov exponents, Poincare mapping, fractal dimension and continuous spectrum. Meanwhile, for further enhancing the complexity of the topological structure of the new chaotic attractors, the attractors are changed from two-wing to four-wing through making axis doubly polarized, theoretically analyzed and numerically simulated. The obtained results clearly show that the chaotic system deserves further detailed investigation.
On the Separability of Attractors in Grandmother Dynamic Systems with Structured Connectivity
Costa, L F
2007-01-01
The combination of complex networks and dynamic systems research is poised to yield some of the most interesting theoretic and applied scientific results along the forthcoming decades. The present work addresses a particularly important related aspect, namely the quantification of how well separated can the attractors be in dynamic systems underlined by four types of complex networks (Erd\\H{o}s-R\\'enyi, Barab\\'asi-Albert, Watts-Strogatz and as well as a geographic model). Attention is focused on grandmother dynamic systems, where each state variable (associated to each node) is used to represent a specific prototype pattern (attractor). By assuming that the attractors spread their influence among its neighboring nodes through a diffusive process, it is possible to overlook the specific details of specific dynamics and focus attention on the separability among such attractors. This property is defined in terms of two separation indices (one individual to each prototype and the other considering also the immedi...
Controlling chaos system by using adaptive fuzzy method based on terminal attractor
International Nuclear Information System (INIS)
An adaptive fuzzy method with terminal attractor based on input-output linearization for a class of uncertain chaos systems is presented. It controls the strong nonlinear chaos systems validly and rapidly for introducing the concept of terminal attractors that has the properties of stability and fast convergence. Global stability of the controller is established. Two kinds of chaos systems are controlled by using this approach. The results of simulation demonstrate the validity and rapidity of the method
Multivalued Attractors and their Approximation: Applications to the Navier-Stokes equations
Zelati, Michele Coti
2011-01-01
This article is devoted to the study of multivalued semigroups and their asymptotic behavior, with particular attention to iteration of set-valued mappings. After developing a general abstract framework, we present an application to the two-dimensional Navier-Stokes equations. More precisely, we prove that the fully implicit Euler scheme generates a family of discrete multivalued dynamical systems, whose global attractors converge to the global attractor of the continuous system as the time-step parameter approaches zero.
Experimental observation of strange nonchaotic attractors in a driven excitable system
International Nuclear Information System (INIS)
We report the observation of strange nonchaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange nonchaotic behaviors in the anodic current were generated. The inception of strange nonchaotic attractors was verified using standard diagnostic techniques
Different routes to chaos via strange nonchaotic attractor in a quasiperiodically forced system
Venkatesan, A.; Lakshmanan, M
1998-01-01
This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are shown to be realizable in the same model over a two parameters ($f-\\epsilon$) domain of the system. In particular, the transition through torus doubling to chaos via SNA, torus breaking to chaos via SNA and period doubling bifurcations of fractal torus are d...
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: 0.844, year: 2014 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf
Chaotic inflation limits for non-minimal models with a Starobinsky attractor
International Nuclear Information System (INIS)
We investigate inflationary attractor points by analysing non-minimally coupled single field inflation models in two opposite limits; the 'flat' limit in which the first derivative of the conformal factor is small and the 'steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in φ2n-chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is shown to be related to the flatness condition on the conformal factor. We stress that the chaotic attractor behaviour in the weak coupling limit is of a different, less universal, character than the Starobinsky attractor. Agreement with the COBE normalisation cannot be obtained in both attractor limits at the same time and in the chaotic attractor limit the scale of inflation depends on the details of the conformal factor, contrary to the strong coupling Starobinsky attractor
The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong
2007-01-01
Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor(UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
International Nuclear Information System (INIS)
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
Emenheiser, Jeffrey; Chapman, Airlie; Pósfai, Márton; Crutchfield, James P.; Mesbahi, Mehran; D'Souza, Raissa M.
2016-09-01
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.
Noncommutative D3-brane, black holes, and attractor mechanism
International Nuclear Information System (INIS)
We revisit the 4D generalized black hole geometries, obtained by us 14, with a renewed interest, to unfold some aspects of effective gravity in a noncommutative D3-brane formalism. In particular, we argue for the existence of extra dimensions in the gravity decoupling limit in the theory. We show that the theory is rather described by an ordinary geometry and is governed by an effective string theory in 5D. The extremal black hole geometry AdS5 obtained in effective string theory is shown to be in precise agreement with the gravity dual proposed for D3-brane in a constant magnetic field. Kaluza-Klein compactification is performed to obtain the corresponding charged black hole geometries in 4D. Interestingly, they are shown to be governed by the extremal black hole geometries known in string theory. The attractor mechanism is exploited in effective string theory underlying a noncommutative D3-brane and the macroscopic entropy of a charged black hole is computed. We show that the generalized black hole geometries in a noncommutative D3-brane theory are precisely identical to the extremal black holes known in 4D effective string theory
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.
Gu, Anhui; Li, Yangrong
2014-01-01
We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both det...
Directory of Open Access Journals (Sweden)
Javier Jas
2010-01-01
Full Text Available Previous studies showed that the finger Photoplethysmographic (PPG signal contains several dynamically distinct components. This work is focused on the characterization of the low-dimensional nonlinear component of the PPG signal.Nine young (5-22 years of age and ten adult (30-91 y presumptively healthy subjects were recorded during 10 minutes in supine position. Each individual traces was divided into non-overlapping segments each with 500 data points, and kernel nonlinear estimation was performed. Noise free Realizations (NFR were generated for each nonlinearly estimated segment.We obtained that 72.8% (657 out of 902 analyzed NFR of the NFR were periodic, corresponding to limit cycle attractors. Besides, 14.4% of the attractors were chaotic, and 7.4% of the NFR corresponded to point attractors. In 47 NFR (5.2% the appearance was either periodic or chaotic, but their amplitude was less than 10% of the original trace. We classified these traces as 'quasi-punctual'. Thus, besides previously described periodic attractors, chaotic, quasi-punctual and point attractors may be found. Proportions for each type of attractors varied among subjects, and periodic attractors were more abundant among older subjects (p<0.05.We interpret these results as an evidence of maturation of the nonlinear cardiovascular dynamics. We stress that the contribution of stochastic influences into the PPG signal cannot be omitted. Limit cycle dynamics apparently warranties a better robustness of the system. Since PPG's stochastic component is a fractal motion, the study of the interaction between this fractal component and the low-dimensional nonlinear system need to be theoretically handled to understand their implications for cardiovascular physiology.
Detecting a Singleton Attractor in a Boolean Network Utilizing SAT Algorithms
Tamura, Takeyuki; Akutsu, Tatsuya
The Boolean network (BN) is a mathematical model of genetic networks. It is known that detecting a singleton attractor, which is also called a fixed point, is NP-hard even for AND/OR BNs (i.e., BNs consisting of AND/OR nodes), where singleton attractors correspond to steady states. Though a naive algorithm can detect a singleton attractor for an AND/OR BN in O(n 2n) time, no O((2-ε)n) (ε > 0) time algorithm was known even for an AND/OR BN with non-restricted indegree, where n is the number of nodes in a BN. In this paper, we present an O(1.787n) time algorithm for detecting a singleton attractor of a given AND/OR BN, along with related results. We also show that detection of a singleton attractor in a BN with maximum indegree two is NP-hard and can be polynomially reduced to a satisfiability problem.
Structure and evolution of strange attractors in non-elastic triangular billiards
Arroyo, Aubin; Sanders, David P
2011-01-01
We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\\lambda$ is varied. For $\\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fra...
Li, Qin; Wennborg, Anders; Aurell, Erik; Dekel, Erez; Zou, Jie-Zhi; Xu, Yuting; Huang, Sui; Ernberg, Ingemar
2016-03-01
The observed intercellular heterogeneity within a clonal cell population can be mapped as dynamical states clustered around an attractor point in gene expression space, owing to a balance between homeostatic forces and stochastic fluctuations. These dynamics have led to the cancer cell attractor conceptual model, with implications for both carcinogenesis and new therapeutic concepts. Immortalized and malignant EBV-carrying B-cell lines were used to explore this model and characterize the detailed structure of cell attractors. Any subpopulation selected from a population of cells repopulated the whole original basin of attraction within days to weeks. Cells at the basin edges were unstable and prone to apoptosis. Cells continuously changed states within their own attractor, thus driving the repopulation, as shown by fluorescent dye tracing. Perturbations of key regulatory genes induced a jump to a nearby attractor. Using the Fokker-Planck equation, this cell population behavior could be described as two virtual, opposing influences on the cells: one attracting toward the center and the other promoting diffusion in state space (noise). Transcriptome analysis suggests that these forces result from high-dimensional dynamics of the gene regulatory network. We propose that they can be generalized to all cancer cell populations and represent intrinsic behaviors of tumors, offering a previously unidentified characteristic for studying cancer. PMID:26929366
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.
SRB measures for a class of partially hyperbolic attractors in Hilbert spaces
Lian, Zeng; Liu, Peidong; Lu, Kening
2016-07-01
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is Hölder continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and the splitting is Hölder continuous, then there exist at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set.
Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys
Institute of Scientific and Technical Information of China (English)
Pierluigi COLLI; Michel FR(E)MOND; Elisabetta ROCCA; Ken SHIRAKAWA
2006-01-01
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely,we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.
Controllable V-Shape Multi-Scroll Butterfly Attractor: System and Circuit Implementation
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.
International Nuclear Information System (INIS)
In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincaré map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations are in good agreement with the numerical simulation results. (general)
A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system
International Nuclear Information System (INIS)
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization. (general)
A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system
Institute of Scientific and Technical Information of China (English)
Dong En-Zeng; Chen Zai-Ping; Chen Zeng-Qiang; Yuan Zhu-Zhi
2009-01-01
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies.Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.
Existence of the solutions and the attractors for the large-scale atmospheric equations
Institute of Scientific and Technical Information of China (English)
HUANG; Haiyang; GUO; Boling
2006-01-01
In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik's definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.
Dyonic AdS_4 black hole entropy and attractors via entropy function
Goulart, Prieslei
2015-01-01
Using the Sen's entropy function formalism, we compute the entropy for the extremal dyonic black hole solutions of theories in the presence of dilaton field coupled to the field strength and a dilaton potential. We solve the attractor equations analytically and determine the near horizon metric, the value of the scalar fields and the electric field on the horizon, and consequently the entropy of these black holes. The attractor mechanism plays a very important role for these systems, and after studying the simplest systems involving dilaton fields, we propose a general ansatz for the value of the scalar field on the horizon, which allows us to solve the attractor equations for gauged supergravity theories in AdS_4 spaces.
A signature of attractor dynamics in the CA3 region of the hippocampus.
Directory of Open Access Journals (Sweden)
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.
Araújo, Vitor; Melbourne, Ian
2015-01-01
We prove exponential decay of correlations for a class of $C^{1+\\alpha}$ uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.
Existence of exponential attractors for the plate equations with strong damping
Directory of Open Access Journals (Sweden)
Qiaozhen Ma
2013-05-01
Full Text Available We show the existence of $(H_0^2(Omegaimes L^2(Omega, H_0^2(Omegaimes H_0^2(Omega$-global attractors for plate equations with critical nonlinearity when $gin H^{-2}(Omega$. Furthermore we prove that for each fixed $T > 0$, there is an ($H_0^2(Omegaimes L^2(Omega, H_0^2(Omegaimes H_0^2(Omega_{T}$-exponential attractor for all $gin L^2(Omega$, which attracts any $H_0^2(Omegaimes L^2(Omega$-bounded set under the stronger $H^2(Omegaimes H^2(Omega$-norm for all $tgeq T$.
On whether zero is in the global attractor of the 2D Navier–Stokes equations
International Nuclear Information System (INIS)
The set of nonzero external forces for which the zero function is in the global attractor of the two-dimensional Navier–Stokes equations is shown to be meagre in a Fréchet topology. A criterion in terms of a Taylor expansion in complex time is used to characterize the forces in this set. This leads to several relations between certain Gevrey subclasses of C∞ and a new upper bound for a Gevrey norm of solutions in the attractor, valid in the strip of analyticity in time. (paper)
Experimental observation of strange non-chaotic attractors in a driven excitable system
International Nuclear Information System (INIS)
We report the observation of strange non-chaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange non-chaotic behaviors in the anodic current were generated. The inception of strange non-chaotic attractors was verified using standard diagnostic techniques
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...
Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks
Directory of Open Access Journals (Sweden)
Chuangxia Huang
2016-01-01
Full Text Available We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI, and the average dwell time approach (ADT, some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.
On coincidence problem and attractor solutions in ELKO dark energy model
Sadjadi, H Mohseni
2011-01-01
We study the critical points of a Universe dominated by ELKO spinor field dark energy and a barotropic matter in an almost general case. The coincidence problem and attractor solutions are discussed and it is shown the coincidence problem can not be alleviated in this model.
Nonlinear attractor dynamics in the fundamental and extended prism adaptation paradigm
Energy Technology Data Exchange (ETDEWEB)
Frank, T.D. [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)], E-mail: frank@uconn.edu; Blau, Julia J.C. [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States); Turvey, M.T. [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States); Haskins Laboratories, New Haven, CT 06510 (United States)
2009-03-09
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.
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…
Chromatin remodeling system, cancer stem-like attractors, and cellular reprogramming.
Zhang, Yue; Moriguchi, Hisashi
2011-11-01
The cancer cell attractors theory provides a next-generation understanding of carcinogenesis and natural explanation of punctuated clonal expansions of tumor progression. The impressive notion of atavism of cancer is now updated but more evidence is awaited. Besides, the mechanisms that the ectopic expression of some germline genes result in somatic tumors such as melanoma and brain tumors are emerging but are not well understood. Cancer could be triggered by cells undergoing abnormal cell attractor transitions, and may be reversible with "cyto-education". From mammals to model organisms like Caenorhabditis elegans and Drosophila melanogaster, the versatile Mi-2β/nucleosome remodeling and histone deacetylation complexes along with their functionally related chromatin remodeling complexes (CRCs), i.e., the dREAM/Myb-MuvB complex and Polycomb group complex are likely master regulators of cell attractors. The trajectory that benign cells switch to cancerous could be the reverse of navigation of embryonic cells converging from a series of intermediate transcriptional states to a final adult state, which is supported by gene expression dynamics inspector assays and some cross-species genetic evidence. The involvement of CRCs in locking cancer attractors may help find the recipes of perturbing genes to achieve successful reprogramming such that the reprogrammed cancer cell function in the same way as the normal cells. PMID:21909785
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 poi...
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...
Nonlinear attractor dynamics in the fundamental and extended prism adaptation paradigm
International Nuclear Information System (INIS)
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
Colwell, Robert K; Gotelli, Nicholas J; Ashton, Louise A; Beck, Jan; Brehm, Gunnar; Fayle, Tom M; Fiedler, Konrad; Forister, Matthew L; Kessler, Michael; Kitching, Roger L; Klimes, Petr; Kluge, Jürgen; Longino, John T; Maunsell, Sarah C; McCain, Christy M; Moses, Jimmy; Noben, Sarah; Sam, Katerina; Sam, Legi; Shapiro, Arthur M; Wang, Xiangping; Novotny, Vojtech
2016-09-01
We introduce a novel framework for conceptualising, quantifying and unifying discordant patterns of species richness along geographical gradients. While not itself explicitly mechanistic, this approach offers a path towards understanding mechanisms. In this study, we focused on the diverse patterns of species richness on mountainsides. We conjectured that elevational range midpoints of species may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favourability. The midpoint attractor interacts with geometric constraints imposed by sea level and the mountaintop to produce taxon-specific patterns of species richness. We developed a Bayesian simulation model to estimate the location and strength of the midpoint attractor from species occurrence data sampled along mountainsides. We also constructed midpoint predictor models to test whether environmental variables could directly account for the observed patterns of species range midpoints. We challenged these models with 16 elevational data sets, comprising 4500 species of insects, vertebrates and plants. The midpoint predictor models generally failed to predict the pattern of species midpoints. In contrast, the midpoint attractor model closely reproduced empirical spatial patterns of species richness and range midpoints. Gradients of environmental favourability, subject to geometric constraints, may parsimoniously account for elevational and other patterns of species richness. PMID:27358193
From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks
Tian, Daxin; Zhou, Jianshan; Sheng, Zhengguo; Wang, Yunpeng; Ma, Jianming
2016-03-01
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.
Exact analytic self-similar solution of a wave attractor field
Maas, L.
2009-01-01
Stratified and rotating fluids support obliquely propagating internal waves. A symmetry-breaking shape of the fluid domain focuses them on a wave attractor. For a trapezoidal basin, it is here shown how to determine the internal wave field analytically. This requires solving the wave equation on a c
The global attractor of the 2D Boussinesq equations with fractional Laplacian in Subcritical case
Huang, Aimin; Huo, Wenru
2015-01-01
We prove global well-posedness of strong solutions and existence of the global attractor for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and temperature.
Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise
Energy Technology Data Exchange (ETDEWEB)
Shu, Ji, E-mail: shuji2008@hotmail.com, E-mail: 530282863@qq.com; Li, Ping, E-mail: shuji2008@hotmail.com, E-mail: 530282863@qq.com; Zhang, Jia; Liao, Ou [College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066 (China)
2015-10-15
This paper is concerned with the stochastic coupled fractional Ginzburg-Landau equation with additive noise. We first transform the stochastic coupled fractional Ginzburg-Landau equation into random equations whose solutions generate a random dynamical system. Then we prove the existence of random attractor for random dynamical system.
Detecting small attractors of large Boolean networks by function-reduction-based strategy.
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. PMID:26997659
Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise
International Nuclear Information System (INIS)
This paper is concerned with the stochastic coupled fractional Ginzburg-Landau equation with additive noise. We first transform the stochastic coupled fractional Ginzburg-Landau equation into random equations whose solutions generate a random dynamical system. Then we prove the existence of random attractor for random dynamical system
Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes
International Nuclear Information System (INIS)
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 AdS2×S3 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 AdS2×S3 geometries can in turn be connected to AdS5 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 AdS5 spacetime. The asymptotic AdS5 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
Khanmamedov, Azer
2010-01-01
In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\\Omega)\\times L_{2}(\\Omega) and then it is proved that this global attractor is a bounded subset of H^{2}(\\Omega)\\times H^{2}(\\Omega) and also a global attractor in H^{2}(\\Omega)\\cap H_{0}^{1}(\\Omega)\\times H_{0}^{1}(\\Omega).
On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0
International Nuclear Information System (INIS)
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 A0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier-Stokes-α model converges to the trajectory attractor A0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit Amin(subset or equal A0) of the trajectory attractor Aα as α→0+ and prove that the set Amin is connected and strictly invariant. Bibliography: 35 titles.
International Nuclear Information System (INIS)
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 Φ6 Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined
Timoudas, Thomas Ohlson
2015-01-01
Let $\\Phi$ be a quasi-periodically forced quadratic map, where the rotation constant $\\omega$ is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under $\\Phi$) attracting graph of a nowhere continuous measurable function $\\psi$ from the circle $\\mathbb{T}$ to $[0,1]$. This paper investigates how a smooth attractor degenerates into a strange one, as a parameter $\\beta$ approaches a critical value $\\beta_0$, and the asymptotics behind the bifurcation of the attra...
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.
International Nuclear Information System (INIS)
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
Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit
International Nuclear Information System (INIS)
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
Trajectory attractor for a non-autonomous Magnetohydrodynamic equations of Non-Newtonian Fluids
Razafimandimby, Paul Andre
2011-01-01
In this article we initiate the mathematical study of the dynamics of a system of nonlinear Partial Differential Equations modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We mainly prove the existence of weak solutions to the model. We also prove the existence of a trajectory attractor to the translation semigroup acting on the trajectories of the set of weak solutions and that of external forces. Some results concerning the structure of this trajectory attractor are also given. The results from this paper may be useful in the investigation of some system of PDEs arising from the coupling of incompressible fluids of $p$-structure and the Maxwell equations.
Existence of exponential attractors for the plate equations with strong damping
Qiaozhen Ma; Yun Yang; Xiaoliang Zhang
2013-01-01
We show the existence of $(H_0^2(Omega)imes L^2(Omega), H_0^2(Omega)imes H_0^2(Omega))$-global attractors for plate equations with critical nonlinearity when $gin H^{-2}(Omega)$. Furthermore we prove that for each fixed $T > 0$, there is an ($H_0^2(Omega)imes L^2(Omega), H_0^2(Omega)imes H_0^2(Omega))_{T}$-exponential attractor for all $gin L^2(Omega)$, which attracts any $H_0^2(Omega)imes L^2(Omega)$-bounded set under the stronger $H^2(Omega)imes H^2(Omega)$-norm for all $tgeq T$.
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.
The Uniform Attractors for the Nonhomogeneous 2D Navier-Stokes Equations in Some Unbounded Domain
Directory of Open Access Journals (Sweden)
Delin Wu
2008-03-01
Full Text Available We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain ÃŽÂ© with nonhomogeneous boundary conditions. We apply the so-called uniformly ÃÂ‰-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming fÃ¢ÂˆÂˆLloc2((0,T;L2(ÃŽÂ©, which is translation compact and ÃÂ†Ã¢ÂˆÂˆCb1(Ã¢Â„Â+;H2(Ã¢Â„Â1ÃƒÂ—{Ã‚Â±L} asymptotically almost periodic, we establish the existence of the uniform attractor in H1(ÃŽÂ©.
The de Sitter spacetime as an attractor solution in fourth-order gravity
International Nuclear Information System (INIS)
We investigate the general vacuum solution of fourth-order gravity, and include the Bach tensor. For L2 = 1.3μR2 + 1/2αC2 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)
A SAT-based algorithm for finding attractors in synchronous Boolean networks.
Dubrova, Elena; Teslenko, Maxim
2011-01-01
This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible. PMID:21778527
The in-phase states of Josephson junctions stacks as attractors
International Nuclear Information System (INIS)
The aim of this investigation is to show that the coherent, in-phase states of intrinsic Josephson junctions stacks are attractors of the stacks' states when the applied external magnetic field he and the external current γ vary within certain domains. Mathematically the problem is to find the solutions of the system of perturbed sine-Gordon equations for fixed other parameters and zero or random initial conditions. We determine the region in the plane (he, γ), where the in-phase states are attractors of the stack's states for arbitrary initial perturbations. This is important, because the in-phase states are required for achieving terahertz radiation from the Josephson stacks
Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit
Kengne, J.; Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.; Nguomkam Negou, A.
2015-10-01
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.
Decomposing the "strange attractor like" seismic electric precursor into simpler components
Thanassoulas, C; Verveniotis, G; Zymaris, N
2009-01-01
An attempt is made in this work to decompose the "strange attractor like" seismic electric precursor into more simple and elementary components. The basic data files of the orthogonal (NS, EW) components of the Earth's electric field used for the compilation of the corresponding phase maps are decomposed by a joint non-linear inversion scheme into two basic oscillating electric fields. The first one, called "signal", is attributed to a single current source while the second, called "noise", is attributed to the mix-up of some regional and randomly located current sources. The comparison of the phase maps compiled from the raw data files to the ones compiled by the "signal" and "noise" data shows that the newly compiled "strange attractor like" phase maps preserve their predictive property while their appearance resembles simpler geometrical shapes (pure hyperbolas and ellipses). Moreover, it is postulated that its generating mechanism is the stress waves applied in the regional area by the combined interactio...
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.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-07-01
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.
Induced gravity and the attractor dynamics of dark energy/dark matter
Cervantes-Cota, Jorge L; de Putter, Roland; 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...
Effect of synapse dilution on the memory retrieval in structured attractor neural networks
BRUNEL,N
1993-01-01
We investigate a simple model of structured attractor neural network (ANN). In this network a module codes for the category of the stored information, while another group of neurons codes for the remaining information. The probability distribution of stabilities of the patterns and the prototypes of the categories are calculated, for two different synaptic structures. The stability of the prototypes is shown to increase when the fraction of neurons coding for the category goes down. Then the ...
'I noticed': the emergence of self-observation in relationship to pathological attractor sites.
Busch, Fred
2007-04-01
The author highlights self-observation as an important goal of psychoanalysis, separate from other concepts with which it is often confounded. To support this position, he presents clinical and developmental data, as well as observations by psychoanalysts on recent findings by cognitive neuroscientists. He introduces the term 'pathological attractor sites' to capture the challenge in moving from the belief in the reality of one's own thoughts to self-observation. Clinical techniques to deal with this specific challenge are presented. PMID:17392058
Non-invasive attractor reconstruction analysis for early detection of deteriorations
Charlton, Peter Harcourt; Camporota, Luigi; Smith, John; Nandi, Manasi; Christie, Mark Ian; Aston, Philip; Beale, Richard
2015-01-01
Acutely-ill hospital patients are at risk of clinical deteriorations. Attractor reconstruction (AR) analysis of the arterial blood pressure (ABP) signal has recently been proposed as a method for measuring the changes in cardiovascular state which accompany deteriorations. Since ABP signals are only available in a minority of clinical scenarios, we sought to determine whether AR could also be performed on more widely available pulse oximetry (photoplethysmogram, PPG) signals. AR analysis was ...
Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay
International Nuclear Information System (INIS)
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
A Hybrid Oscillatory Interference/Continuous Attractor Network Model of Grid Cell Firing
Bush, D.; Burgess, N.
2014-01-01
Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account fo...
Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations
Cheban, David; Duan, Jinqiao
2004-01-01
The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic,almost automorphic, recurrent, pseudo recurrent) solutions of non-autono...
A Mathematical Model of Chaotic Attractor in Tumor Growth and Decay
Ivancevic, Tijana T.; Bottema, Murk J.; Jain, Lakhmi C.
2008-01-01
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance, as well as in temporal behavior. This is clearly a characteristic of dynamical systems sensitive to initial conditions. The new chaotic model of tumor growth and decay is biologically motivated. It has been developed as a live Mathematica demonstration, see...
Control of confidence domains in the problem of stochastic attractors synthesis
International Nuclear Information System (INIS)
A nonlinear stochastic control system is considered. We discuss a problem of the synthesis of stochastic attractors and suggest a constructive approach based on the design of the stochastic sensitivity and corresponding confidence domains. Details of this approach are demonstrated for the problem of the control of confidence ellipses near the equilibrium. An example of the control for stochastic Van der Pol equation is presented
V.-T. Pham; Ch. K. Volos; S. Vaidyanathan; T. P. Le; V. Y. Vu
2014-01-01
Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention recently. A memristor-based hyperchaotic system with hidden attractor is studied in this paper. The dynamics properties of this hyperchaotic system are discovered through equilibria, Lyapunov exponents, bifurcation diagram, Poincaré map and limit cycles. In addition, its anti-synchronization scheme via adaptive cont...
Coupled chaotic attractors and driving-induced bistability: A brief review
Indian Academy of Sciences (India)
Manish Agrawal
2015-02-01
We investigate the effects of symmetry-preserving and symmetry-breaking interactions n a drive–response system with the driving-induced bistability. The basins of attraction on the initial conditions plane are observed for the driving-induced bistability. The basins are dependent on the interaction between the driven and the driving system. The coexisting attractors display both in-phase as well as antiphase synchrony.
Smooth Attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities
Kalantarov, VK; Zelik, S.
2011-01-01
We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an arbitrary polynomial growth rate. In order to obtain this result, we prove the maximal regularity estimate for the corresponding semi-linear stationary Stokes problem using some modification of the nonlinear localization technique. The applications of our results to the Brinkmann-Forchheimer equation with the Navier-Stokes inertial term are also ...
A Model Combining Oscillations and Attractor Dynamics for Generation of Grid Cell Firing
Michael E Hasselmo; Brandon, Mark P.
2012-01-01
Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interference of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units ...
Phase-space analysis of the cosmological 3-fluid problem: Families of attractors and repellers
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 $\\gamma-1$, a pressureless dark matter fluid, plus a scalar field $\\phi$ (representing dark energy) coupled to exponential potential $V=V_0\\exp{(-\\kappa\\lambda\\phi)}$. Besides the potential-kinetic-scaling solutions, which are not the unique late-time attractors whenever they exist for $\\lambda^2\\geq 3\\ga$, 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 $\\ga >1$. The case of a pressureless barotropic fluid ($\\ga=1$) 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.
Directory of Open Access Journals (Sweden)
Paul Miller
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.
Strange Attractors in the Vannimenus Model on an Arbitrary Order Cayley Tree
International Nuclear Information System (INIS)
We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uguz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.
Dynamics of entanglement and 'attractor' states in the Tavis-Cummings model
Jarvis, C. E. A.; Rodrigues, D. A.; Györffy, B. L.; Spiller, T. P.; Short, A. J.; Annett, J. F.
2009-10-01
We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at {\\textstyle\\frac{t_{r}}{4}} , halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes-Cummings model (JCM) and we therefore generalize the discovery by Gea-Banacloche for the one-qubit case. We give the 'basin of attraction' for Nq qubits and discuss the implications of the 'attractor' state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.
Dynamics of Entanglement and `Attractor' states in The Tavis-Cummings Model
Jarvis, C E A; Györffy, B L; Spiller, T P; Short, A J; Annett, J F
2009-01-01
We study the time evolution of $N_q$ two-level atoms (or qubits) interacting with a single mode of the quantised radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at $\\sfrac{t_r}{4}$, halfway between that start of the collapse and the first mini revival peak, where $t_r$ is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an `attractor state'. The set itself is termed the basin of attraction and the features are at the center of our attention. Extending to more qubits, we find that attractors are a generic feature of the multi qubit Jaynes Cummings model (JCM) and we therefore generalise the discovery by Gea-Banacloche for the one qubit case. We give the `basin of attraction' for $N_q$ qubits and discuss the implications of the `attractor' state in terms of the dynamics of $N_q$-body entanglement. We observe both collapse a...
Geiyer, Daniel; Kauffman, Jeffrey L.
2016-04-01
Research in broadband nonlinear piezoelectric energy harvesting has gained traction in recent years as resonant, linear harvesters do not operate optimally in dynamic environments. By placing a linear harvester in a symmetric magnetic field, a nonlinear restoring force allows the system to realize motion across two potential wells. Different levels of excitation enable the system to oscillate solely in one potential well, periodically across both potential wells, or aperiodically across both potential wells. Periodic interwell motion is considered desirable for nonlinear energy harvesting systems, however, coexistent attractors inhibit uniqueness of such a solution. The authors have previously shown that chaotic, aperiodic motion between potential wells can be optimized for improved energy harvesting. The technique applied a chaotic controller to stabilize a large amplitude periodic orbit within the chaotic attractor. This work considers the basins of attraction of the two concurrent attractors and applies an intermittent control law in which the system is perturbed from a chaotic, aperiodic interwell response into the desirable large amplitude, periodic, interwell response.
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.
Dynamics of entanglement and 'attractor' states in the Tavis-Cummings model
International Nuclear Information System (INIS)
We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at tr/4, halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes-Cummings model (JCM) and we therefore generalize the discovery by Gea-Banacloche for the one-qubit case. We give the 'basin of attraction' for Nq qubits and discuss the implications of the 'attractor' state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.
Dimensional reduction of BPS attractors in AdS gauged supergravities
Hristov, Kiril
2014-01-01
We relate across dimensions BPS attractors of black strings and black holes of various topology in gauged supergravities with nontrivial scalar potential. The attractors are of the form AdS$_{2, 3} \\times \\Sigma^{2, 3}$ in 4, 5, and 6 dimensions, and can be generalized to some higher dimensional analogs. Even though the attractor geometries admit standard Kaluza-Klein and Scherk-Schwarz reductions, their asymptotic AdS spaces in general do not. The resulting lower dimensional objects are black holes with runaway asymptotics in supergravity theories with no maximally symmetric vacua. Such classes of solutions are already known to exist in literature, and results here suggest an interpretation in terms of their higher-dimensional origin that often has a full string theory embedding. In a particular relevant example, the relation between 5d Benini-Bobev black strings arXiv:1302.4451 and a class of 4d Cacciatori-Klemm black holes arXiv:0911.4926 is worked out in full detail, providing a type IIB and dual field th...
Institute of Scientific and Technical Information of China (English)
Fu-qi Yin; Sheng-fan Zhou
2006-01-01
In this paper, we establish the existence of a global attractor for a coupled k-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-Schrodinger Equation. An estimate of the upper bound of the Kolmogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented .
Audio-Visual Attractors for Capturing Attention to the Screens When Walking in CAVE Systems
Grani, Francesco; Argelaguet Sanz, Ferran; Gouranton, Valérie; Badawi, Marwan; Gaugne, Ronan; Serafin, Stefania; Lécuyer, Anatole
2014-01-01
International audience In four-sided CAVE-like VR systems, the absence of the rear wall has been shown to decrease the level of immersion and can introduce breaks in presence. In this paper it is investigated to which extent user's attention can be driven by visual and auditory stimuli in a four-sided CAVE-like system. An experiment was conducted in order to analyze how user attention is diverted while physically walking in a virtual environment, when audio and/or visual attractors are pre...