WorldWideScience

Sample records for attractors

  1. Hot Attractors

    CERN Document Server

    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.

  2. Rotating attractors

    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

  3. 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.

  4. Bayesian Attractor Learning

    Science.gov (United States)

    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.

  5. Hidden attractors in dynamical systems

    Science.gov (United States)

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

    2016-06-01

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

  6. 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.

  7. Attractors in Black

    CERN Document Server

    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...

  8. Inverse Symmetric Inflationary Attractors

    CERN Document Server

    Odintsov, S D

    2016-01-01

    We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...

  9. 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.

  10. Power Spectrum of Inflationary Attractors

    NARCIS (Netherlands)

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

    2015-01-01

    Inflationary attractors predict the spectral index and tensor-to-scalar ratio to take specific values that are consistent with Planck. An example is the universal attractor for models with a generalised non-minimal coupling, leading to Starobinsky inflation. In this paper we demonstrate that it also

  11. Unity of cosmological inflation attractors.

    Science.gov (United States)

    Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik

    2015-04-10

    Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These models, which we call ξ attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T models) and their generalization to α attractors. The aim of this Letter is to elucidate the common denominator of these attractors: their robust predictions stem from a joint pole of order 2 in the kinetic term of the inflaton field in the Einstein frame formulation prior to switching to the canonical variables. Model-dependent differences only arise at subleading level in the kinetic term. As a final step towards the unification of the different attractors, we introduce a special class of ξ attractors which is fully equivalent to α attractors with the identification α=1+(1/6ξ). While r is generically predicted to be of the order 1/N^{2}, there is no theoretical lower bound on r in this class of models.

  12. Controlling Strange Attractor in Dynamics

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

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

  13. Inflationary Attractor from Tachyonic Matter

    CERN Document Server

    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.

  14. Inflationary attractor from tachyonic matter

    Science.gov (United States)

    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.

  15. Inflation, Universality and Attractors

    CERN Document Server

    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...

  16. Moduli Backreaction on Inflationary Attractors

    CERN Document Server

    Roest, Diederik; Werkman, Pelle

    2016-01-01

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

  17. Cosmological attractors in massive gravity

    CERN Document Server

    Dubovsky, S; Tkachev, I I

    2005-01-01

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

  18. Multiple hydrological attractors under stochastic daily forcing: 2. Can multiple attractors emerge?

    Science.gov (United States)

    Peterson, T. J.; Western, A. W.; Argent, R. M.

    2014-04-01

    The companion paper showed that multiple steady state groundwater levels can exist within a hill-slope Boussinesq-vegetation model under daily stochastic forcing. Using a numerical limit-cycle continuation algorithm, the steady states (henceforth attractors) and the threshold between them (henceforth repellor) were quantified at a range of saturated lateral conductivity values, ksmax. This paper investigates if stochastic daily forcing can switch the catchment between both of the attractors. That is, an attractor may exist under average forcing conditions but can stochastic forcing switch the catchment into and out of each of the attractor basins?; i.e., making the attractor emerge. This was undertaken using the model of the companion paper and by completing daily time-integration simulations at six values of the saturated lateral hydraulic conductivity, ksmax; three having two attractors and three having only a deep water table attractor. By graphically analyzing the simulations, and comparing against simulations from a model modified to have only one attractor, multiple attractors were found to emerge under stochastic daily forcing. However, the emergence of attractors was significantly more subtle and complex than that suggested by the companion paper. That is, an attractor may exist but never emerge; both attractors may exist and both may emerge but identifying the switching between attractors was often ambiguous; and only one attractor may exist and but a second temporary attractor may exist and emerge during periods of high precipitation. This subtle and complex emergence of attractors was explained using continuation analysis of the climate forcing rate, and not a model parameter such as ksmax. It showed that the temporary attractor existed over a large range of ksmax values and this suggests that more catchments may have multiple attractors than suggested by the companion paper. By combining this continuation analysis with the time-integration simulations

  19. Intermittent control of coexisting attractors.

    Science.gov (United States)

    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

  20. Hyperbolic geometry of cosmological attractors

    NARCIS (Netherlands)

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

    2015-01-01

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

  1. Temporal attractors for speech onsets

    Science.gov (United States)

    Port, Robert; Oglesbee, Eric

    2003-10-01

    When subjects say a single syllable like da in time with a metronome, what is the easiest relationship? Superimposed on the metronome pulse, of course. The second easiest way is probably to locate the syllable halfway between pulses. We tested these hypotheses by having subjects repeat da at both phase angles at a range of metronome rates. The vowel onset (or P-center) was automatically obtained for each token. In-phase targets were produced close to the metronome onset for rates as fast as 3 per second. Antiphase targets were accurate at slow rates (~2/s) but tended to slip to inphase timing with faster metronomes. These results resemble the findings of Haken et al. [Biol. Cybern. 51, 347-356 (1985)] for oscillatory finger motions. Results suggest a strong attractor for speech onsets at zero phase and a weaker attractor at phase 0.5 that may disappear as rate is increased.

  2. More on N=8 Attractors

    CERN Document Server

    Ceresole, A; Gnecchi, A; Marrani, A

    2009-01-01

    We examine few simple extremal black hole configurations of N=8, d=4 supergravity. We first elucidate the relation between the BPS Reissner-Nordstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N=8 supergravity.

  3. Dark Energy from $\\alpha$-Attractors

    CERN Document Server

    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.

  4. Strange attractor simulated on a quantum computer

    OpenAIRE

    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.

  5. Inflation as AN Attractor in Scalar Cosmology

    Science.gov (United States)

    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.

  6. Non-minimal coupling and inflationary attractors

    CERN Document Server

    Yi, Zhu

    2016-01-01

    We show explicitly how the T-model, E-model and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $\\xi$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.

  7. Black Hole Attractors in Extended Supergravity

    CERN Document Server

    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.

  8. Wild attractors and thermodynamic formalism

    CERN Document Server

    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...

  9. 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)

  10. Supersymmetry, attractors and cosmic censorship

    CERN Document Server

    Bellorin, J; Ortín, T; Bellorin, Jorge; Meessen, Patrick; Ortin, Tomas

    2006-01-01

    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 absence of sources of 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 in the explicit knowledge of the most genera...

  11. STU attractors from vanishing concurrence

    CERN Document Server

    Lévay, Péter

    2010-01-01

    Concurrence is an entanglement measure characterizing the {\\it mixed} state bipartite correlations inside of a pure state of an $n$-qubit system. We show that after organizing the charges and the moduli in the STU model of $N=2$, $d=4$ supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the {\\it pure} state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.

  12. Decaying turbulence and developing chaotic attractors

    CERN Document Server

    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.

  13. 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

  14. 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.

  15. 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.

  16. Singular-hyperbolic attractors are chaotic

    OpenAIRE

    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...

  17. Supersymmetry, attractors and cosmic censorship

    Science.gov (United States)

    Bellorín, Jorge; Meessen, Patrick; Ortín, Tomás

    2007-01-01

    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.

  18. 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.

  19. Multiple hydrological attractors under stochastic daily forcing: 1. Can multiple attractors exist?

    Science.gov (United States)

    Peterson, T. J.; Western, A. W.

    2014-04-01

    Including positive feedbacks in hydrological models has recently been shown to result in complex behavior with multiple steady states. When a large disturbance, say a major drought, is simulated within such models the hydrology changes. Once the disturbance ends the hydrology does not return to that prior to the disturbance, but rather, persists within an alternate state. These multiple steady states (henceforth attractors) exist for a single model parameterization and cause the system to have a finite resilience to such transient disturbances. A limitation of past hydrological resilience studies is that multiple attractors have been identified using mean annual or mean monthly forcing. Considering that most hydrological fluxes are subject to significant forcing stochasticity and do not operate at such large timescales, it remains an open question whether multiple hydrological attractors can exist when a catchment is subject to stochastic daily forcing. This question is the focus of this paper and it needs to be addressed prior to searching for multiple hydrological attractors in the field. To investigate this, a previously developed semidistributed hillslope ecohydrological model was adopted which exhibited multiple steady states under average monthly climate forcing. In this paper, the ecohydrological model was used to explore if feedbacks between the vegetation and a saline water table result in two attractors existing under daily stochastic forcing. The attractors and the threshold between them (henceforth repellor) were quantified using a new limit cycle continuation technique that upscaled climate forcing from daily to monthly (model and limit cycle code is freely available). The method was used to determine the values of saturated lateral hydraulic conductivity at which multiple attractors exist. These estimates were then assessed against time-integration estimates, which they agreed with. Overall, multiple attractors were found to exist under stochastic

  20. Terminal attractors for addressable memory in neural networks

    Science.gov (United States)

    Zak, Michail

    1988-01-01

    A new type of attractors - terminal attractors - for an addressable memory in neural networks operating in continuous time is introduced. These attractors represent singular solutions of the dynamical system. They intersect (or envelope) the families of regular solutions while each regular solution approaches the terminal attractor in a finite time period. It is shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the weight matrix.

  1. Strange attractor simulated on a quantum computer

    CERN Document Server

    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...

  2. 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.

  3. GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES

    Institute of Scientific and Technical Information of China (English)

    戴正德; 杜先云

    2001-01-01

    In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.

  4. Homogenization of attractors for a class of nonlinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    WANG Guo-lian; ZHANG Xing-you

    2004-01-01

    The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.

  5. Erice Lectures on Black Holes and Attractors

    CERN Document Server

    Ferrara, Sergio; Marrani, A

    2008-01-01

    These lectures give an elementary introduction to the subject of four dimensional black holes (BHs) in supergravity and the Attractor Mechanism in the extremal case. Some thermodynamical properties are discussed and some relevant formulae for the critical points of the BH effective potential are given. The case of Maxwell-Einstein-axion-dilaton (super)gravity is discussed in detail. Analogies among BH entropy and multipartite entanglement of qubits in quantum information theory, as well moduli spaces of extremal BH attractors, are also discussed.

  6. Random attractors for asymptotically upper semicompact multivalue random semiflows

    Institute of Scientific and Technical Information of China (English)

    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.

  7. Cosmological Attractors from $α$-Scale Supergravity

    NARCIS (Netherlands)

    Roest, Diederik; Scalisi, Marco

    2015-01-01

    The Planck value of the spectral index can be interpreted as $n_s = 1 - 2/N$ in terms of the number of e-foldings $N$. An appealing explanation for this phenomenological observation is provided by $\\alpha$-attractors: the inflationary predictions of these supergravity models are fully determined by

  8. Noise-enhanced reconstruction of attractors

    CERN Document Server

    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.

  9. Attractor black holes and quantum distribution functions

    Energy Technology Data Exchange (ETDEWEB)

    Montanez, S. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gomez, C. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Theory Group, Physics Department, CERN, 1211 Geneva 23 (Switzerland)

    2007-05-15

    Using the attractor mechanism and the wavefunction interpretation of the topological string partition function on a Calabi Yau threefold M we study the relation between the Bekenstein-Hawking-Wald entropy of BPS Calabi-Yau black holes and quantum distribution functions defined on H{sup 3}(M). We discuss the OSV conjecture in this context. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  10. Single-field $\\alpha$-attractors

    CERN Document Server

    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.

  11. Large Global Coupled Maps with Multiple Attractors

    CERN Document Server

    Carusela, M F; Romanelli, L

    1999-01-01

    A system of N unidimensional global coupled maps (GCM), which support multiattractors is studied. We analize the phase diagram and some special features of the transitions (volume ratios and characteristic exponents), by controlling the number of elements of the initial partition that are in each basin of attraction. It was found important difference with widely known coupled systems with a single attractor.

  12. The Hyperbolic Geometry of Cosmological Attractors

    NARCIS (Netherlands)

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

    2015-01-01

    Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into

  13. Single-field α-attractors

    Energy Technology Data Exchange (ETDEWEB)

    Linde, Andrei [Department of Physics and SITP, Stanford University,Stanford, California 94305 (United States)

    2015-05-05

    I describe a simple class of α-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for 0<α≲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.

  14. Cosmological attractors from alpha-scale supergravity

    NARCIS (Netherlands)

    Roest, Diederik; Scalisi, Marco

    2015-01-01

    The Planck value of the spectral index can be interpreted as n(s) = 1 - 2/N in terms of the number of e-foldings N. An appealing explanation for this phenomenological observation is provided by alpha-attractors: the inflationary predictions of these supergravity models are fully determined by the cu

  15. Semicontinuity of attractors for impulsive dynamical systems

    Science.gov (United States)

    Bonotto, E. M.; Bortolan, M. C.; Collegari, R.; Czaja, R.

    2016-10-01

    In this paper we introduce the concept of collective tube conditions which assures a suitable behaviour for a family of dynamical systems close to impulsive sets. Using the collective tube conditions, we develop the theory of upper and lower semicontinuity of global attractors for a family of impulsive dynamical systems.

  16. ATTRACTORS FOR THE BRUSSELATOR IN RN

    Institute of Scientific and Technical Information of China (English)

    Han Yongqian; Guo Boling

    2007-01-01

    We consider the reaction-diffusion system, a model of a certain chemical morphogenetic process and named Brusselator. For the Cauchy problem of this system with nondecaying initial data, the existence and uniqueness of the global solution is established. Moreover, it is proved that this system possesses a global attractor A in the corresponding phase space.

  17. 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

  18. Tiling Spaces, Codimension One Attractors and Shape

    CERN Document Server

    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.

  19. Sneutrino Inflation with $\\alpha$-attractors

    CERN Document Server

    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.

  20. Gravitational waves in $\\alpha-$attractors

    CERN Document Server

    Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna

    2015-01-01

    We study inflation in the $\\alpha-$attractor model under a non-slow-roll dynamics with an ansatz proposed by Gong \\& Sasaki \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. Under this approach, we construct a class of local shapes of inflaton potential that are different from the T-models. We find this type of inflationary scenario predicts an attractor at $n_{s}\\sim0.967$ and $r\\sim0.00055$. In our approach, the non-slow-roll inflaton dynamics are related to the $\\alpha-$parameter which is the curvature of K\\"ahler geometry in the SUGRA embedding of this model.

  1. Evidence for attractors in English intonation.

    Science.gov (United States)

    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

  2. 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.

  3. Exponential Attractor for a Nonlinear Boussinesq Equation

    Institute of Scientific and Technical Information of China (English)

    Ahmed Y. Abdallah

    2006-01-01

    This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H20(0, 1) × L2(0, 1). The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H03(0, 1) × H10(0, 1).

  4. Cortical attractor network dynamics with diluted connectivity.

    Science.gov (United States)

    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

  5. Hypermoduli Stabilization, Flux Attractors, and Generating Functions

    CERN Document Server

    Larsen, Finn; Robbins, Daniel

    2009-01-01

    We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be integrated by a generating function with the property that the hypermoduli are determined by a simple extremization principle. We work out several orbifold examples where all vector moduli and many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.

  6. ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Mu-rong Jiang; Bo-ling Guo

    2001-01-01

    In this paper, Ginzburg-Landau equation coupled with BBM equationwith periodic initial boundary value conditions are discreted by the finite difference method in spatial direction. Existence of the attractors for the spatially discreted Ginzburg-Landau-BBM equations is proved. For each mesh size, there exist attractors for the discretized system. Moreover, finite Hausdorff and fractal dimensions of the discrete attractors are obtained and the bounds are independent of the mesh sizes.

  7. METHODOLOGICAL NOTES: Strange attractors in rattleback dynamics

    Science.gov (United States)

    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.

  8. Dimensions of attractors in pinched skew products

    CERN Document Server

    Gröger, M

    2011-01-01

    We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.

  9. 3rd School on Attractor Mechanism

    CERN Document Server

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

    2010-01-01

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

  10. 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.

  11. 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.

  12. Energy cascade in internal wave attractors

    CERN Document Server

    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.

  13. 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

  14. TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY

    Institute of Scientific and Technical Information of China (English)

    Yonghai WANG; Lingzhi WANG

    2013-01-01

    In this article,we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory.For this purpose,we will apply the method presented by Chepyzhov and Miranville [7,8],in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.

  15. Synchronization in Coupled Oscillators with Two Coexisting Attractors

    Institute of Scientific and Technical Information of China (English)

    ZHU Han-Han; YANG Jun-Zhong

    2008-01-01

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

  16. 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.

  17. Hidden attractor in the Rabinovich system, Chua circuits and PLL

    Science.gov (United States)

    Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Seledzhi, S. M.

    2016-06-01

    In this report the existence of hidden attractors in Rabinovich system, phase-locked loop and coupled Chua circuits is considered. It is shown that the existence of hidden attractors may complicate the analysis of the systems and significantly affect the synchronization.

  18. 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

  19. Extremal Black Hole and Flux Vacua Attractors

    CERN Document Server

    Bellucci, S; Kallosh, R; Marrani, A

    2007-01-01

    These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\\frac{CY_{3}\\times T^{2}}{\\mathbb{Z}_{2}}$. Finally, recent...

  20. On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau's and attractor equations

    Science.gov (United States)

    Kaura, P.; Misara, A.

    2006-12-01

    We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY_3(2,128) expressed as a degree-12 hypersurface in WCP^4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the attractors could be connected to an elliptic curve fibered over C^8 which may also be "arithmetic" (in some cases, it is possible to interpret the extremization conditions as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that the attractors correspond to a version of A_1-singularity in the space Image(Z^6-->R^2/Z_2(embedded in R^3)) fibered over the complex structure moduli space. The potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP^5-->CP^{20}, fibered over the complex structure moduli space. We also discuss application of the equivalent Kallosh's attractor equations for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the atractor equations than the extremization of the black hole potential.

  1. The past attractor in inhomogeneous cosmology

    CERN Document Server

    Uggla, C; Wainwright, J; Ellis, G F R; Uggla, Claes; Elst, Henk van; Wainwright, John; Ellis, George F R

    2003-01-01

    We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein's field equations with a perfect fluid matter source as an autonomous system of evolution equations and constraints. This framework incorporates spatially homogeneous dynamics in a natural way as a special case, thereby placing earlier work on spatially homogeneous cosmology in a broader context, and allows us to draw on experience gained in that field using dynamical systems methods. One of our goals is to provide a precise formulation of the approach to the spacelike initial singularity in cosmological models, described heuristically by Belinski\\v{\\i}, Khalatnikov and Lifshitz. Specifically, we construct an invariant set which we conjecture forms the local past attractor for the evolution equations. We anticipate that this new formulation will provide the basis for ...

  2. 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.

  3. Strange Attractor in Immunology of Tumor Growth

    CERN Document Server

    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.

  4. Oscillatory Attractors: A New Cosmological Phase

    CERN Document Server

    Bains, Jasdeep S; Wilczek, Frank

    2015-01-01

    In expanding FRW spacetimes, it is usually the case that homogeneous scalar fields redshift and their amplitudes approach limiting values: Hubble friction usually ensures that the field relaxes to its minimum energy configuration, which is usually a static configuration. Here we discover a class of relativistic scalar field models in which the attractor behavior is the field oscillating indefinitely, with finite amplitude, in an expanding FRW spacetime, despite the presence of Hubble friction. This is an example of spontaneous breaking of time translation symmetry. We find that the effective equation of state of the field has average value $\\langle w\\rangle=-1$, implying that the field itself could drive an inflationary or dark energy dominated phase. This behavior is reminiscent of ghost condensate models, but in the new models, unlike in the ghost condensate models, the energy-momentum tensor is time dependent, so that these new models embody a more definitive breaking of time translation symmetry. We explo...

  5. 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.

  6. IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    马军海; 任彪; 陈予恕

    2004-01-01

    Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.

  7. 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)

  8. Embeddings of a strange attractor into R3.

    Science.gov (United States)

    Tsankov, Tsvetelin D; Nishtala, Arunasri; Gilmore, Robert

    2004-05-01

    The algorithm for determining a global Poincaré section is applied to a previously studied dynamical system on R2 x S1 and a one-parameter family of embeddings of the strange attractor it generates into R3. We find that the topological properties of the attractor are embedding dependent to a limited extent. These embeddings rigidly preserve mechanism, which is a simple stretch and fold. The embeddings studied show three discrete topological degrees of freedom: parity, global torsion, and braid type of the genus-one torus bounding the embedded attractor. PMID:15244912

  9. 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...

  10. Features from the non-attractor beginning of inflation

    CERN Document Server

    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.

  11. Investigating the Rossler Attractor Using Lorentz Plot and Lyapunov Exponents

    OpenAIRE

    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.

  12. A Hyperchaotic Attractor Coined from Chaotic Lu System

    Institute of Scientific and Technical Information of China (English)

    BAO Bo-Cheng; LIU Zhong

    2008-01-01

    We report a new hyperchaotic attractor coined from the chaotic Lu system by using a state feedback controller. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviour of the proposed hyperchaotic system.

  13. 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.

  14. Passive control of chaotic system with multiple strange attractors

    Institute of Scientific and Technical Information of China (English)

    Song Yun-Zhong; Zhao Guang-Zhou; Qi Dong-Lian

    2006-01-01

    In this paper we present a new simple controller for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form.Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, 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 suggested method.

  15. 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)

  16. Strange Attractors Characterizing the Osmotic Instability

    CERN Document Server

    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...

  17. Nonnuclear Attractors in Heteronuclear Diatomic Systems.

    Science.gov (United States)

    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

  18. 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.

  19. Hippocampal Attractor Dynamics Predict Memory-Based Decision Making.

    Science.gov (United States)

    Steemers, Ben; Vicente-Grabovetsky, Alejandro; Barry, Caswell; Smulders, Peter; Schröder, Tobias Navarro; Burgess, Neil; Doeller, Christian F

    2016-07-11

    Memories are thought to be retrieved by attractor dynamics if a given input is sufficiently similar to a stored attractor state [1-5]. The hippocampus, a region crucial for spatial navigation [6-12] and episodic memory [13-18], has been associated with attractor-based computations [5, 9], receiving support from the way rodent place cells "remap" nonlinearly between spatial representations [19-22]. In humans, nonlinear response patterns have been reported in perceptual categorization tasks [23-25]; however, it remains elusive whether human memory retrieval is driven by attractor dynamics and what neural mechanisms might underpin them. To test this, we used a virtual reality [7, 11, 26-28] task where participants learned object-location associations within two distinct virtual reality environments. Participants were subsequently exposed to four novel intermediate environments, generated by linearly morphing the background landscapes of the familiar environments, while tracking fMRI activity. We show that linear changes in environmental context cause linear changes in activity patterns in sensory cortex but cause dynamic, nonlinear changes in both hippocampal activity pattern and remembered locations. Furthermore, the sigmoidal response in the hippocampus scaled with the strength of the sigmoidal pattern in spatial memory. These results indicate that mnemonic decisions in an ambiguous novel context relate to putative attractor dynamics in the hippocampus, which support the dynamic remapping of memories. PMID:27345167

  20. Coexistence of exponentially many chaotic spin-glass attractors.

    Science.gov (United States)

    Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I

    2011-12-01

    A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.

  1. Attractor Solutions in Lorentz Violating Scalar-Vector-Tensor Theory

    CERN Document Server

    Arianto, Freddy P; Triyanta,; Gunara, Bobby E

    2008-01-01

    We investigate properties of attractors for scalar field in the Lorentz violating scalar-vector-tensor theory of gravity. In this framework, both the effective coupling and potential functions determine the stabilities of the fixed points. In the model, we consider the constants of slope of the effective coupling and potential functions which lead to the quadratic effective coupling vector with the (inverse) power-law potential. For the case of purely scalar field, there are only two stable attractor solutions in the inflationary scenario. In the presence of a barotropic fluid, the fluid dominated solution is absent. We find two scaling solutions: the kinetic scaling solution and the scalar field scaling solutions. We show the stable attractors in regions of ($\\gamma$, $\\xi$) parameter space and in phase plane plot for different qualitative evolutions. From the standard nucleosynthesis, we derive the constraints for the value of the coupling parameter.

  2. Separation of attractors in 1-modulus quantum corrected special geometry

    CERN Document Server

    Bellucci, S; Marrani, A; Shcherbakov, A

    2008-01-01

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

  3. Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics

    Energy Technology Data Exchange (ETDEWEB)

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

    2011-02-28

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

  4. Global attractors of a degenerate parabolic equation and their error estimates

    Institute of Scientific and Technical Information of China (English)

    HU Xiaohong; ZHANG Xingyou

    2004-01-01

    The existences of the global attractor A? for a degenerate parabolic equation and of the homogenized attractorA0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between A? and A0 are given.

  5. Compact Global Chaotic Attractors of Discrete Control Systems

    Directory of Open Access Journals (Sweden)

    Cheban David

    2014-01-01

    Full Text Available The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fv(n(xn, where v: Z+ → {1; 2; : : : ;m}. If m≥2 we give sufficient conditions (the family M := {f1; f2; : : : ; fm} of functions is contracting in the extended sense for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles

  6. 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.

  7. Uniform attractors of non-autonomous dissipative semilinear wave equations

    Institute of Scientific and Technical Information of China (English)

    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.

  8. Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.

    Science.gov (United States)

    Klarner, Hannes; Siebert, Heike

    2015-01-01

    This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.

  9. 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.

  10. Multistability and hidden attractors in a relay system with hysteresis

    DEFF Research Database (Denmark)

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

    2015-01-01

    For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the nei...

  11. Global attractors for damped abstract nonlinear hyperbolic systems

    Science.gov (United States)

    Pinter, Gabriella Agnes

    1997-12-01

    This dissertation is concerned with the long time dynamics of a class of damped abstract hyperbolic systems that arise in the study of certain smart material structures, namely elastomers. The term smart material refers to a material capable of both sensing and responding actively to outside excitation. These properties make smart materials a prime canditate for actuation and sensing in next generation control systems. However, modeling and numerically simulating their behavior poses several difficulties. In this work we consider a model for elastomers developed by H. T. Banks, N. J. Lybeck, B. C. Munoz, L. C. Yanyo, formulate this model as an abstract evolution system, and study the long time behavior of its solutions. We remark that the question of existence and uniqueness of solutions for this class of systems is a challenging problem and was only recently solved by H. T. Banks, D. S. Gilliam and V. I. Shubov. Concerning the long time dynamics of the problem, we first prove that the system generates a weak dynamical system, and possesses a weak global attractor. Our main result is the existence of a "strong" dynamical system which has a compact global attractor. With the help of a Lyapunov function we are able to characterize the structure of this attractor. We also give a theorem that guarantees the stability of the global attractor with respect to varying parameters in the system. Our last result concerns the uniform differentiability of the dynamical system.

  12. 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.

  13. A non-reward attractor theory of depression.

    Science.gov (United States)

    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

  14. On the Supersymmetry of Bianchi attractors in Gauged supergravity

    CERN Document Server

    Chakrabarty, Bidisha; Samanta, Rickmoy

    2016-01-01

    Bianchi attractors are near horizon geometries with homogeneous symmetries in the spatial directions. We construct supersymmetric Bianchi attractors in $\\mathcal{N}=2, d=4,5$ gauged supergravity coupled to vector and hypermultiplets. In $d=4$, in the Bianchi I class we construct an electric $1/4$ BPS $AdS_2\\times\\mathbb{R}^2$ geometry. In $d=5$ we consider gauged supergravity with a generic gauging of symmetries of the scalar manifold and the R symmetry. Analyzing the gaugino and hyperino conditions we show that when the fermionic shifts do not vanish there are no supersymmetric Bianchi attractors. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold be ungauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In the Bianchi I class we show that the anisotropic $AdS_3\\times\\mathbb{R}^2$ solution is $1/2$ BPS. We also construct a new clas...

  15. Non-slow-roll dynamics in $\\alpha-$attractors

    CERN Document Server

    Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna

    2015-01-01

    In this paper we consider the $\\alpha-$attractor model and study inflation under a generalization of slow-roll dynamics. We follow the recently proposed Gong \\& Sasaki approach \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. We relax the requirement of inflaton potential flatness and consider a sufficiently steep one to support 60-efoldings. We find that this type of inflationary scenario predicts an attractor at $n_{s}\\approx0.967$ and $r\\approx5.5\\times10^{-4}$ which are very close to the predictions of the first chaotic inflationary model in supergravity (Goncharov-Linde model) \\cite{Goncharov:1983mw}. We show that even with non-slow-roll dynamics, the $\\alpha-$attractor model is compatible with any value of $r<0.1$. In addition, we emphasize that in this particular inflationary scenario, the standard consistency relation $\\left(r\\simeq-8n_{t}\\right)$ is significantly violated and we find an attractor for tensor tilt at $n_{t}\\approx-0.034$ as $r\\rightarrow0$. Any prominent detection of the ...

  16. Attractors for stochastic lattice dynamical systems with a multiplicative noise

    Institute of Scientific and Technical Information of China (English)

    Tomás CARABALLO; Kening LU

    2008-01-01

    In this paper,we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction,a dissipative nonlinear reaction term,and multiplicative white noise at each node.We prove the existence of a compact global random attractor which,pulled back,attracts tempered random bounded sets.

  17. GLOBAL ATTRACTOR OF NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES

    Institute of Scientific and Technical Information of China (English)

    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.

  18. Dynamical movement primitives: learning attractor models for motor behaviors.

    Science.gov (United States)

    Ijspeert, Auke Jan; Nakanishi, Jun; Hoffmann, Heiko; Pastor, Peter; Schaal, Stefan

    2013-02-01

    Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

  19. Potential flux landscapes determine the global stability of a Lorenz chaotic attractor under intrinsic fluctuations.

    Science.gov (United States)

    Li, Chunhe; Wang, Erkang; Wang, Jin

    2012-05-21

    We developed a potential flux landscape theory to investigate the dynamics and the global stability of a chemical Lorenz chaotic strange attractor under intrinsic fluctuations. Landscape was uncovered to have a butterfly shape. For chaotic systems, both landscape and probabilistic flux are crucial to the dynamics of chaotic oscillations. Landscape attracts the system down to the chaotic attractor, while flux drives the coherent motions along the chaotic attractors. Barrier heights from the landscape topography provide a quantitative measure for the robustness of chaotic attractor. We also found that the entropy production rate and phase coherence increase as the molecular numbers increase. Power spectrum analysis of autocorrelation function provides another way to quantify the global stability of chaotic attractor. We further found that limit cycle requires more flux and energy to sustain than the chaotic strange attractor. Finally, by detailed analysis we found that the curl probabilistic flux may provide the origin of the chaotic attractor.

  20. Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency.

    Science.gov (United States)

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

    2013-06-01

    We experimentally study strange nonchaotic attractors (SNAs) and chaotic attractors by using a nonlinear integrated circuit driven by a quasiperiodic input signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. It is a difficult problem to distinguish between SNAs and chaotic attractors experimentally. If a system has an SNA as a unique attractor, the system produces an identical response to a repeated quasiperiodic signal, regardless of the initial conditions, after a certain transient time. Such reproducibility of response outputs is called consistency. On the other hand, if the attractor is chaotic, the consistency is low owing to the sensitive dependence on initial conditions. In this paper, we analyze the experimental data for distinguishing between SNAs and chaotic attractors on the basis of the consistency.

  1. Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons.

    Science.gov (United States)

    Yu, Jiali; Yi, Zhang; Zhou, Jiliu

    2010-10-01

    Continuous attractors of Lotka-Volterra recurrent neural networks (LV RNNs) with infinite neurons are studied in this brief. A continuous attractor is a collection of connected equilibria, and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on many factors such as the connectivity and the external inputs of the network. A continuous attractor can be stable or unstable. It is shown in this brief that a LV RNN can possess multiple continuous attractors if the synaptic connections and the external inputs are Gussian-like in shape. Moreover, both stable and unstable continuous attractors can coexist in a network. Explicit expressions of the continuous attractors are calculated. Simulations are employed to illustrate the theory.

  2. Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach

    Science.gov (United States)

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

    2015-12-01

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

  3. 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.)

  4. 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)

  5. Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization

    CERN Document Server

    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.

  6. A chaotic attractor in timing noise from the Vela pulsar?

    Science.gov (United States)

    Harding, Alice K.; Shinbrot, Troy; Cordes, James M.

    1990-01-01

    Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

  7. Generating multi-double-scroll attractors via nonautonomous approach.

    Science.gov (United States)

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

    2016-08-01

    It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method. PMID:27586606

  8. 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)

  9. Generating multi-double-scroll attractors via nonautonomous approach

    Science.gov (United States)

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

    2016-08-01

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

  10. A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

    Institute of Scientific and Technical Information of China (English)

    HU Guo-Si

    2009-01-01

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

  11. Measurement of cardiovascular state using attractor reconstruction analysis

    OpenAIRE

    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...

  12. 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)

  13. Attractors and chaos of electron dynamics in electromagnetic standing wave

    CERN Document Server

    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.

  14. CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    Li Yuhong; Zdzistaw Brze(z)niak; Zhou Jianzhong

    2008-01-01

    The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.

  15. Global attractors and extinction dynamics of cyclically competing species

    Science.gov (United States)

    Rulands, Steffen; Zielinski, Alejandro; Frey, Erwin

    2013-05-01

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

  16. 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.

  17. Pattern Selection in Network of Coupled Multi-Scroll Attractors.

    Science.gov (United States)

    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.

  18. 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.

  19. Pattern Selection in Network of Coupled Multi-Scroll Attractors

    Science.gov (United States)

    Li, Fan

    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

  20. High-dimensional chaotic and attractor systems a comprehensive introduction

    CERN Document Server

    Ivancevic, Vladimir G

    2007-01-01

    This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. The book has nine Chapters. The first Chapter gives a textbook-like introduction into the low-dimensional attractors and chaos. This Chapter has an inspirational character, similar to other books on nonlinear dynamics and deterministic chaos. The second Chapter deals with Smale’s topological transformations of stretching, squeezing and folding (of the system’s phase–space), developed for the purpose of chaos theory. The third Chapter is devoted to Poincaré's 3-body problem and basic techniques of chaos control, mostly of Ott-Grebogi-Yorke type. The fourth Chapter is a review of both Landau’s and topological phase transition theory, as w...

  1. An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.

    Science.gov (United States)

    He, Qinbin; Xia, Zhile; Lin, Bin

    2016-11-01

    Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.

  2. Continuous or discrete attractors in neural circuits? A self-organized switch at maximal entropy

    CERN Document Server

    Bernacchia, Alberto

    2007-01-01

    A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled by distinct forms of synaptic prescriptions (learning rules). Here, we report a solvable network model, endowed with Hebbian synaptic plasticity, which is able to learn either discrete or continuous attractors, depending on the frequency of presentation of stimuli and on the structure of sensory coding. A continuous attractor is learned when experience matches sensory coding, i.e. when the distribution of experienced stimuli matches the distribution of preferred stimuli of neurons. In that case, there is no processing of sensory information and neural activity displays maximal entropy. If experience goes beyond sensory coding, processing is initiated and the continuous attractor is destabilized into a set of discrete attractors.

  3. 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.

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

    Institute of Scientific and Technical Information of China (English)

    Qu Shi-Xian; Lu Yong-Zhi; Zhang Lin; He Da-Ren

    2008-01-01

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

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

    DEFF Research Database (Denmark)

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

    2015-01-01

    The term `hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point......, this paper describes the formation of several different coexisting sets of hidden attractors, including the simultaneous presence of a pair of coinciding quasiperiodic attractors and of two mutually symmetric chaotic attractors. We follow the dynamics of the system as a function of the basic oscillator...

  6. On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds

    CERN Document Server

    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.

  7. MAXIMAL ATTRACTORS OF CLASSICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH DISPERSION

    Institute of Scientific and Technical Information of China (English)

    Li Yanling; Ma Yicheng

    2005-01-01

    The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region.Finally, a few examples of application are given.

  8. Is attentional blink a byproduct of neocortical attractors?

    Directory of Open Access Journals (Sweden)

    David N Silverstein

    2011-05-01

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

  9. Universal fractional map and cascade of bifurcations type attractors.

    Science.gov (United States)

    Edelman, M

    2013-09-01

    We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional αbifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.

  10. 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.

  11. 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.

  12. 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.

  13. Global Attractor for Damped Wave Equations with Nonlinear Memory

    Institute of Scientific and Technical Information of China (English)

    Yinghao HAN; Zhen'guo YU; Zhengguo JIN

    2012-01-01

    Let Ω (C) Rn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt + αut - △u - ∫t0μ(t - s)|u(s)|βu(s)ds + g(u) =f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10 (Ω) × L2 (Ω).

  14. 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.

  15. Experimental exploration of the optomechanical attractor diagram and its dynamics

    CERN Document Server

    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.

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

    Science.gov (United States)

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

    2015-01-01

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

  17. Lorenz-like attractors in a nonholonomic model of a rattleback

    Science.gov (United States)

    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.

  18. Kolmogorov's ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems

    Institute of Scientific and Technical Information of China (English)

    Sheng Fan ZHOU; Qiu Li JIA; Wei SHI

    2007-01-01

    We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov's ε-entropy of the global attractor for lattice systems.

  19. 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.

  20. Sustainability as global attractor: the greening of the 2008 Beijing Olympics

    NARCIS (Netherlands)

    Mol, A.P.J.

    2010-01-01

    If one interprets sustainability as an attractor, it means that across time and place notions and ideas of sustainability structure, order and pattern institutions and practices. One can effectively explore the idea that sustainability is turning into a global attractor through mega events. As high

  1. Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

    CERN Document Server

    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...

  2. Attractor scenarios and superluminal signals in k-essence cosmology

    CERN Document Server

    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...

  3. Sensory feedback in a bump attractor model of path integration.

    Science.gov (United States)

    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

  4. Sensory feedback in a bump attractor model of path integration.

    Science.gov (United States)

    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.

  5. 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)

  6. ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.

    Science.gov (United States)

    Kobayashi, Koichi; Hiraishi, Kunihiko

    2014-01-01

    Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.

  7. 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

  8. Attractor for a Reaction-Diffusion System Modeling Cancer Network

    Directory of Open Access Journals (Sweden)

    Xueyong Chen

    2014-01-01

    Full Text Available A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω×L2(Ω and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.

  9. Broken Scale Invariance, Alpha-Attractors and Vector Impurity

    CERN Document Server

    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.

  10. The Hot Attractor Mechanism: Decoupling Without Deep Throats

    CERN Document Server

    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.

  11. Strange Attractors in Multipath propagation Detection and characterisation

    CERN Document Server

    Tannous, C; Angus, A G

    2001-01-01

    Multipath propagation of radio waves in indoor/outdoor environments shows a highly irregular behavior as a function of time. Typical modeling of this phenomenon assumes the received signal is a stochastic process composed of the superposition of various altered replicas of the transmitted one, their amplitudes and phases being drawn from specific probability densities. We set out to explore the hypothesis of the presence of deterministic chaos in signals propagating inside various buildings at the University of Calgary. The correlation dimension versus embedding dimension saturates to a value between 3 and 4 for various antenna polarizations. The full Liapunov spectrum calculated contains two positive exponents and yields through the Kaplan-Yorke conjecture the same dimension obtained from the correlation sum. The presence of strange attractors in multipath propagation hints to better ways to predict the behaviour of the signal and better methods to counter the effects of interference. The use of Neural Netwo...

  12. Strange attractor of Henon map and its basin

    Institute of Scientific and Technical Information of China (English)

    曹永罗

    1995-01-01

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

  13. How organisms do the right thing: The attractor hypothesis

    Science.gov (United States)

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

    1998-01-01

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

  14. How organisms do the right thing: The attractor hypothesis

    Science.gov (United States)

    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.

  15. 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.

  16. Systematic Computation of the Least Unstable Periodic Orbits in Chaotic Attractors

    CERN Document Server

    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.

  17. Multiple attractors and generalized synchronization in delayed Mackey-Glass systems

    Institute of Scientific and Technical Information of China (English)

    Li Dong; Zheng Zhi-Gang

    2008-01-01

    Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored.Coexistent multiple chaotic attractors are found.Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincaré section.Synchronizations of the drive-response Mackey-Glass oscillators are investigated.The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour.We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers,i.e.,more resonance peaks can be found.

  18. Generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems

    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.

  19. On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau's and attractor equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaura, P. [Indian Institute of Technology Roorkee, Roorkee 247 667, Uttaranchal (India); Misara, A. [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)

    2006-12-15

    We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY{sub 3}(2,128) expressed as a degree-12 hypersurface in WCP{sup 4}[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non-supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C{sup 8} which may also be ''arithmetic'' (in some cases, it is possible to interpret the extremization conditions for the black-hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non-supersymmetric black-hole attractors corresponds to a version of A{sub 1}-singularity in the space Image(Z{sup 6}{yields}R{sup 2}/Z{sub 2}({yields}R{sup 3})) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP{sup 5}{yields}CP{sup 20}, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black-hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  20. Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor

    Institute of Scientific and Technical Information of China (English)

    ALI M.; SAHA L.M.

    2005-01-01

    A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an altemative method to calculate λ1has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.

  1. An in silico target identification using Boolean network attractors: Avoiding pathological phenotypes.

    Science.gov (United States)

    Poret, Arnaud; Boissel, Jean-Pierre

    2014-12-01

    Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.

  2. On the Separability of Attractors in Grandmother Dynamic Systems with Structured Connectivity

    CERN Document Server

    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...

  3. Convergence to the critical attractor of dissipative maps: log-periodic oscillations, fractality, and nonextensivity

    Science.gov (United States)

    de Moura FA; Tirnakli; Lyra

    2000-11-01

    For a family of logisticlike maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase-space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflection of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.

  4. Pullback D-Attractors for A Non-Autonomous Brinkman-Forchheimer System

    Institute of Scientific and Technical Information of China (English)

    Xueli SONG

    2013-01-01

    The asymptotic behavior of solutions of the three-dimensional nonautonomous Brinkman-Forchheimer equation is investigated.And the existence of pullback global attractors in L2(Ω) and H10(Ω) is proved,respectively.

  5. Attractors for the Ginzburg—Landau—BBM Equations in an Unbounded Domain

    Institute of Scientific and Technical Information of China (English)

    BolingGUO; MurongJIANG

    1998-01-01

    In this paper,the long time behavior of the global solutions of the Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,The existence of the maximal attractor is obtained.

  6. Maximal Unstable Dissipative Interval to Preserve Multi-scroll Attractors via Multi-saturated Functions

    Science.gov (United States)

    Díaz-González, Edgar C.; López-Rentería, Jorge-Antonio; Campos-Cantón, Eric; Aguirre-Hernández, Baltazar

    2016-07-01

    In this paper, we present families of piecewise linear systems which are controlled by a continuous piecewise monoparametric control function for the generation of monoparametric families of multi-scroll attractors. Thus, the maximum range of values that the parameter set can take in order to preserve the useful dynamics for generating of multi-scroll attractors is found and it will be called maximal robust dynamics interval. This class of dynamical systems is the result of combining two or more unstable "one-spiral" trajectories. We give necessary and sufficient conditions in order to preserve multi-scroll attractors in terms of a parameter, i.e., a family of multi-scroll attractors is generated by means of a family of switching systems with multiple monoparametric companion matrices. Lastly, we provide an example to show how the developed theory works.

  7. Attractors, statistics and fluctuations of the dynamics of the Schelling's model for social segregation

    Science.gov (United States)

    Cortez, Vasco; Medina, Pablo; Goles, Eric; Zarama, Roberto; Rica, Sergio

    2015-01-01

    Statistical properties, fluctuations and probabilistic arguments are shown to explain the robust dynamics of the Schelling's social segregation model. With the aid of probability density functions we characterize the attractors for multiple external parameters and conditions. We discuss the role of the initial states and we show that, indeed, the system evolves towards well defined attractors. Finally, we provide probabilistic arguments to explain quantitatively the observed behavior.

  8. Multivalued Attractors and their Approximation: Applications to the Navier-Stokes equations

    CERN Document Server

    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.

  9. Embeddings of low-dimensional strange attractors: Topological invariants and degrees of freedom

    OpenAIRE

    Romanazzi, Nicola; Lefranc, Marc; Gilmore, Robert

    2007-01-01

    When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global torsion, and knot type. We discuss how they can change with the embedding. Finally, we show that the mechanism that is responsible for creating chaotic behavior is an invariant of all embeddings. These results apply only to chaotic attractors of genus one, whic...

  10. 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.

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

    Science.gov (United States)

    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.

  12. 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

  13. 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

  14. Continuous scanning trials:Transitioning through the attractor landscape.

    Science.gov (United States)

    Kennedy, Deanna M; Wang, Chaoyi; Panzer, Stefan; Shea, Charles H

    2016-01-01

    Bimanual 1:1 coordination patterns other than in-phase (0°) and anti-phase (180°) have proven difficult to perform even with extended practice. The difficulty has traditionally been attributed to phase attraction that draws the coordination between the limbs towards the bimanual patterns of in-phase and anti-phase and variability associated with the activation and associated proprioceptive signals of non-homologous muscles via crossed and uncrossed cortical pathways. However, recent experiments have demonstrated that a wide range of relative phase and multi-frequency coordination patterns can be effectively produced with only a few minutes of practice when Lissajous or online relative phase information is provided. The present experiment was designed to determine if participants provided Lissajous feedback comprised of continuously transitioning relative phase goals could be effectively performed as the participant navigates through the attractor landscape. The results clearly indicated that participants can effectively produce a large range of supposedly unstable coordination patterns (between 0° and 180° in 1° increments) after only a few minutes of practice. These findings clearly indicate that the perception-action system is fully capable of effectively producing and transitioning through a wide range of bimanual coordination patterns and that the reason for the failure to produce these patterns in previous experiments resides in the perceptual information and attentional requirements typically found in experimental testing environments. PMID:26546133

  15. 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

  16. 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.

  17. Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

    OpenAIRE

    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...

  18. Chaotic inflation limits for non-minimal models with a Starobinsky attractor

    CERN Document Server

    Mosk, Benjamin

    2014-01-01

    We investigate inflationary attractor points by analyzing 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 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,...

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

    Directory of Open Access Journals (Sweden)

    Takashi Kanamaru

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

  20. Structure and evolution of strange attractors in non-elastic triangular billiards

    CERN Document Server

    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...

  1. Flexibility and attractors in context: family emotion socialization patterns and children's emotion regulation in late childhood.

    Science.gov (United States)

    Lunkenheimer, Erika S; Hollenstein, Tom; Wang, Jun; Shields, Ann M

    2012-07-01

    Familial emotion socialization practices relate to children's emotion regulation (ER) skills in late childhood, however, we have more to learn about how the context and structure of these interactions relates to individual differences in children's ER. The present study examined flexibility and attractors in family emotion socialization patterns in three different conversational contexts and their relation to ER in 8-12 year olds. Flexibility was defined as dispersion across the repertoire of discrete emotion words and emotion socialization functions (emotion coaching, dismissing, and elaboration) in family conversation, whereas attractors were defined as the average duration per visit to each of these three emotion socialization functions using state space grid analysis. It was hypothesized that higher levels of flexibility in emotion socialization would buffer children's ER from the presence of maladaptive attractors, or the absence of adaptive attractors, in family emotion conversation. Flexibility was generally adaptive, related to children's higher ER across all contexts, and also buffered children from maladaptive attractors in select situations. Findings suggest that the study of dynamic interaction patterns in context may reveal adaptive versus maladaptive socialization processes in the family that can inform basic and applied research on children's regulatory problems.

  2. Detecting a Singleton Attractor in a Boolean Network Utilizing SAT Algorithms

    Science.gov (United States)

    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.

  3. Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape.

    Science.gov (United States)

    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

  4. Transtibial amputee joint motion has increased attractor divergence during walking compared to non-amputee gait.

    Science.gov (United States)

    Wurdeman, Shane R; Myers, Sara A; Stergiou, Nicholas

    2013-04-01

    The amputation and subsequent prosthetic rehabilitation of a lower leg affects gait. Dynamical systems theory would predict the use of a prosthetic device should alter the functional attractor dynamics to which the system self-organizes. Therefore, the purpose of this study was to compare the largest Lyapunov exponent (a nonlinear tool for assessing attractor dynamics) for amputee gait compared to healthy non-amputee individuals. Fourteen unilateral, transtibial amputees and fourteen healthy, non-amputee individuals ambulated on a treadmill at preferred, self-selected walking speed. Our results showed that the sound hip (p = 0.013), sound knee (p = 0.05), and prosthetic ankle (p = 0.023) have significantly greater largest Lyapunov exponents than healthy non-amputees. Furthermore, the prosthetic ankle has a significantly greater (p = 0.0.17) largest Lyapunov exponent than the sound leg ankle. These findings indicate attractor states for amputee gait with increased divergence. The increased attractor divergence seems to coincide with decreased ability for motor control between the natural rhythms of the individual and those of the prosthetic device. Future work should consider the impact of different prostheses and rehabilitation on the attractor dynamics.

  5. 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.

  6. Novel four-dimensional autonomous chaotic system generating one-, two-, three- and four-wing attractors

    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)

  7. 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)

  8. 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.

  9. Design and implementation of grid multi-scroll fractional-order chaotic attractors.

    Science.gov (United States)

    Chen, Liping; Pan, Wei; Wu, Ranchao; Tenreiro Machado, J A; Lopes, António M

    2016-08-01

    This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

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

    KAUST Repository

    Zidan, Mohammed A.

    2012-07-23

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

  11. Radiation reaction induced spiral attractors in ultra-intense colliding laser beams

    CERN Document Server

    Gong, Z; Shou, Y R; Qiao, B; Chen, C E; Xu, F R; He, X T; Yan, X Q

    2016-01-01

    The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions. For the first time, the properties of fixed points in electron phase-space were analyzed with linear stability theory, showing that center nodes will become attractors if the classical radiation reaction is considered. Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentially near the attractors. The density growth rates are derived theoretically and further verified by particle-in-cell simulations, which can be detected in experiments to explore the effects of radiation reaction qualitatively. The attractor can also facilitate to realize a series of nanometer-scaled flying electron slices via adjusting the colliding laser frequencies.

  12. SRB measures for a class of partially hyperbolic attractors in Hilbert spaces

    Science.gov (United States)

    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.

  13. 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.

  14. Dyonic AdS_4 black hole entropy and attractors via entropy function

    CERN Document Server

    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.

  15. Design and implementation of grid multi-scroll fractional-order chaotic attractors.

    Science.gov (United States)

    Chen, Liping; Pan, Wei; Wu, Ranchao; Tenreiro Machado, J A; Lopes, António M

    2016-08-01

    This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct. PMID:27586620

  16. Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

    CERN Document Server

    Jouve, Laurène

    2014-01-01

    In a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus on to particular structures known as wave attractors. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (2005) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement ...

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

    Directory of Open Access Journals (Sweden)

    Yongjun Li

    2016-01-01

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

  18. Non-BPS Attractors in 5d and 6d Extended Supergravity

    CERN Document Server

    Andrianopoli, L; Marrani, A; Trigiante, M

    2008-01-01

    We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.

  19. Inertial waves in a rotating spherical shell attractors and asymptotic spectrum

    CERN Document Server

    Rieutord, M; Valdettaro, L

    2000-01-01

    We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic equation (Poincar\\'e's equation) satisfied by inviscid solutions. Characteristics are straight lines in a meridional section of the shell, and the mapping shows that, generically, these lines converge towards a periodic orbit which acts like an attractor. We then examine the relation between this characteristic path and eigensolutions of the inviscid problem and show that in a purely two-dimensional problem, convergence towards an attractor means that the associated velocity field is not square-integrable. We give arguments which generalize this result to three dimensions. We then consider the viscous problem and show how viscosity transforms singularities into internal shear layers which in general betray an attractor expected at the eigenfrequency of the mode. We find that there are nested layers, the thinnest and m...

  20. Asymptotic global fast dynamics and attractor fractal dimension of the TDGL-equations of superconductivity

    Science.gov (United States)

    Willie, Robert

    2016-09-01

    In this paper, we study a model system of equations of the time dependent Ginzburg-Landau equations of superconductivity in a Lorentz gauge, in scale of Hilbert spaces E^{α } with initial data in E^{β } satisfying 3α + β ≥ N/2, where N=2,3 is such that the spatial domain of the equations [InlineEquation not available: see fulltext.]. We show in the asymptotic dynamics of the equations, well-posedness of the dynamical system for a global exponential attractor {{U}}subset E^{α } compact in E^{β } if α >β , uniform differentiability of orbits on the attractor in E0\\cong L2, and the existence of an explicit finite bounding estimate on the fractal dimension of the attractor yielding that its Hausdorff dimension is as well finite. Uniform boundedness in (0,∞ )× Ω of solutions in E^{1/2}\\cong H1(Ω ) is in addition investigated.

  1. Hyperbolic chaotic attractor in amplitude dynamics of coupled self-oscillators with periodic parameter modulation

    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...... amplitudes for the two oscillators of each pair undergoes a transformation in accordance with the expanding circle map during each cycle of the process. We start with equations describing the dynamics in terms of complex or real amplitudes and then examine two models based on van der Pol oscillators. One...... variables, portraits of attractors, Lyapunov exponents, etc. The uniformly hyperbolic nature of the attractor in the stroboscopic Poincare map is confirmed for a real-amplitude version of the equations by computations of statistical distribution of angles between stable and unstable manifolds...

  2. 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.

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

    Science.gov (United States)

    Roach, James; Sander, Leonard; Zochowski, Michal

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

  4. 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 $tgeq T$.

  5. On the existence of an exponential attractor for a planar shear flow with Tresca's friction condition

    CERN Document Server

    Łukaszewicz, Grzegorz

    2012-01-01

    We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique global in time solution of the considered problem which is governed by a variational inequality. Our aim is to prove the existence of a global attractor of a finite fractional dimension and of an exponential attractor for the associated semigroup. We use the method of $l$-trajectories. This research is motivated by a problem from lubrication theory.

  6. Maximal Attractors for the m-Dimensional Cahn-Hilliard System

    Institute of Scientific and Technical Information of China (English)

    Wei Nian ZHANG

    2004-01-01

    In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L2(Ω))m and (H2(Ω))m in terms of D. Henry's general theory and from the viewpoint of compactness and absorptivity of semigroups as R. Temam did. After giving the existence and uniqueness of global solutions, we technically restrict our discussion to some subspaces, give estimates with a new graph norm, and obtain the existence of maximal attractors and some properties of them.

  7. Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

    Science.gov (United States)

    Brzeźniak, Z.; Caraballo, T.; Langa, J. A.; Li, Y.; Łukaszewicz, G.; Real, J.

    We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brzeźniak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations.

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

    CERN Document Server

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

    2013-01-01

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

  9. Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

    Directory of Open Access Journals (Sweden)

    Qiuying Lu

    2014-01-01

    Full Text Available We prove the existence of a pullback attractor in L2(ℝn for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.

  10. Chromatin remodeling system, cancer stem-like attractors, and cellular reprogramming.

    Science.gov (United States)

    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

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

    Science.gov (United States)

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

    2016-03-01

    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.

  12. 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.

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

    Science.gov (United States)

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

    2016-04-01

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

  14. Analytical estimates of efficiency of attractor neural networks with inborn connections

    Directory of Open Access Journals (Sweden)

    Solovyeva Ksenia

    2016-01-01

    Full Text Available The analysis is restricted to the features of neural networks endowed to the latter by the inborn (not learned connections. We study attractor neural networks in which for almost all operation time the activity resides in close vicinity of a relatively small number of attractor states. The number of the latter, M, is proportional to the number of neurons in the neural network, N, while the total number of the states in it is 2N. The unified procedure of growth/fabrication of neural networks with sets of all attractor states with dimensionality d=0 and d=1, based on model molecular markers, is studied in detail. The specificity of the networks (d=0 or d=1 depends on topology (i.e., the set of distances between elements which can be provided to the set of molecular markers by their physical nature. The neural networks parameters estimates and trade-offs for them in attractor neural networks are calculated analytically. The proposed mechanisms reveal simple and efficient ways of implementation in artificial as well as in natural neural networks of multiplexity, i.e. of using activity of single neurons in representation of multiple values of the variables, which are operated by the neural systems. It is discussed how the neuronal multiplexity provides efficient and reliable ways of performing functional operations in the neural systems.

  15. 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

  16. Dimension of Maximal Attractors for the m-dimensional Cahn-Hilliard System

    Institute of Scientific and Technical Information of China (English)

    Wei Nian ZHANG

    2005-01-01

    On the basis of the existence of the maximal attractor of the m-dimensional Cahn-Hilliard system in the product spaces (L2(Ω))m and (H2(Ω))m, in this paper, its Hausdorff dimension is estimated by calculating the orthogonal projection of the linear variational operator of the system.

  17. Midpoint attractors and species richness: Modelling the interaction between environmental drivers and geometric constraints.

    Science.gov (United States)

    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

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

    Science.gov (United States)

    Lerner, Itamar; Bentin, Shlomo; Shriki, Oren

    2012-01-01

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

  19. Exact analytic self-similar solution of a wave attractor field

    NARCIS (Netherlands)

    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

  20. The necessity for a time local dimension in systems with time-varying attractors

    DEFF Research Database (Denmark)

    Særmark, Knud H; Ashkenazy, Y; Levitan, J;

    1997-01-01

    We show that a simple non-linear system for ordinary differential equations may possess a time-varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non...

  1. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

    OpenAIRE

    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).

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

    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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-09-01

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

  4. Power law asymptotics in the creation of strange attractors in the quasi-periodically forced quadratic family

    OpenAIRE

    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...

  5. 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.

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

    Science.gov (United States)

    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.

  7. Trajectory attractor for a non-autonomous Magnetohydrodynamic equations of Non-Newtonian Fluids

    CERN Document Server

    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.

  8. Existence of exponential attractors for the plate equations with strong damping

    OpenAIRE

    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 $tgeq T$.

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

  11. Embeddings of low-dimensional strange attractors: topological invariants and degrees of freedom.

    Science.gov (United States)

    Romanazzi, Nicola; Lefranc, Marc; Gilmore, Robert

    2007-06-01

    When a low-dimensional chaotic attractor is embedded in a three-dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: Parity, global torsion, and knot type. We discuss how they can change with the embedding. Finally, we show that the mechanism that is responsible for creating chaotic behavior is an invariant of all embeddings. These results apply only to chaotic attractors of genus one, which covers the majority of cases in which experimental data have been subjected to topological analysis. This means that the conclusions drawn from previous analyses, for example that the mechanism generating chaotic behavior is a Smale horseshoe mechanism, a reverse horseshoe, a gateau roulé, an S -template branched manifold, etc., are not artifacts of the embedding chosen for the analysis. PMID:17677347

  12. A SAT-based algorithm for finding attractors in synchronous Boolean networks.

    Science.gov (United States)

    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

  13. The in-phase states of Josephson junctions stacks as attractors

    Energy Technology Data Exchange (ETDEWEB)

    Hristov, I.; Dimova, S. [Faculty of Mathematics and Informatics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Blvd., 1164 Sofia (Bulgaria); Hristova, R. [Faculty of Mathematics and Informatics, St. Kliment Ohridski University of Sofia, 5 James Bourchier, Blvd., 1164 Sofia (Bulgaria)

    2014-11-12

    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 h{sub e} 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 (h{sub e}, 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.

  14. Attractors of derivative complex Ginzburg-Landau equation in unbounded domains

    Institute of Scientific and Technical Information of China (English)

    GUO Boling; HAN Yongqian

    2007-01-01

    The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg- Landau (DCGL) equation in an unbounded domain ΩС R2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov's ε-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in R2 is detailed studied.

  15. 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

  16. Decomposing the "strange attractor like" seismic electric precursor into simpler components

    CERN Document Server

    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...

  17. 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.

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

    OpenAIRE

    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...

  19. Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations

    OpenAIRE

    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...

  20. 'I noticed': the emergence of self-observation in relationship to pathological attractor sites.

    Science.gov (United States)

    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

  1. Non-invasive attractor reconstruction analysis for early detection of deteriorations

    OpenAIRE

    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 ...

  2. 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.

  3. A Mathematical Model of Chaotic Attractor in Tumor Growth and Decay

    OpenAIRE

    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...

  4. A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating

    OpenAIRE

    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...

  5. On the problem of topological classification of strange attractors of dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Plykin, Romen V [Obninsk State Technical University for Nuclear Power Engineering, Obninsk, Kaluga Region (Russian Federation)

    2002-12-31

    This paper consists of two parts. The first, which is devoted to presenting results of Barge and Watkins, connects the closure of the union of the unstable manifolds of certain 'Smale horseshoes' with Knaster continua and projections on them of Vietoris-van Dantzig solenoids. In the second part the homeomorphism problem for expanding attractors of codimension 1 is solved when the dimension of the manifold generating the dynamical system is greater than two.

  6. A Model Combining Oscillations and Attractor Dynamics for Generation of Grid Cell Firing

    OpenAIRE

    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 ...

  7. Compact attractors for time-periodic age-structured population models

    Directory of Open Access Journals (Sweden)

    Pierre Magal

    2001-10-01

    Full Text Available In this paper we investigate the existence of compact attractors for time-periodic age-structured models. So doing we investigate the eventual compactness of a class of abstract non-autonomous semiflow (non necessarily periodic. We apply this result to non-autonomous age-structured models. In the time periodic case, we obtain the existence of a periodic family of compact subsets that is invariant by the semiflow, and attract the solutions of the system.

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

    Directory of Open Access Journals (Sweden)

    Pradeep Krishnamurthy

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

  9. Solving Stochastic Büchi Games on Infinite Arenas with a Finite Attractor

    Directory of Open Access Journals (Sweden)

    Nathalie Bertrand

    2013-06-01

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

  10. Spiraling attractors and quantum dynamics for a class of long-range magnetic fields

    DEFF Research Database (Denmark)

    Cornean, Horia Decebal; Herbst, Ira; Skibsted, Erik

    We consider the long time behavior of a quantum particle in a 2-D magnetic field which is homogeneous of degree -1. If the field never vanishes, above a certain energy the associated classical dynamical system has a globally attracting periodic orbit in a reduced phase space. For that energy regime......, we construct a simple approximate evolution based on this attractor, and prove that it completely describes the quantum dynamics of our system....

  11. Spiraling attractors and quantum dynamics for a class of long-range magnetic fields

    DEFF Research Database (Denmark)

    Cornean, Horia; Herbst, Ira; Skibsted, Erik

    2007-01-01

    We consider the long time behavior of a quantum particle in a 2D magnetic field which is homogeneous of degree -1. If the field never vanishes, above a certain energy the associated classical dynamical system has a globally attracting periodic orbit in a reduced phase space. For that energy regime......, we construct a simple approximate evolution based on this attractor, and prove that it completely describes the quantum dynamics of our system....

  12. Phase-space analysis of the cosmological 3-fluid problem: Families of attractors and repellers

    CERN Document Server

    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.

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

    Science.gov (United States)

    Guo, Wensheng; Yang, Guowu; Wu, Wei; He, Lei; Sun, Mingyu

    2014-01-01

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

  14. Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes

    CERN Document Server

    Kachru, Shamit; Saha, Arpan; Samanta, Rickmoy; Trivedi, Sandip P

    2013-01-01

    We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or $AdS_2 \\times S^3$ geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or $AdS_2 \\times S^3$ geometries can in turn be connected to $AdS_5$ spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to $AdS_5$ spacetime. The asymptotic $AdS_5$ spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either sp...

  15. An attractor-based complexity measurement for Boolean recurrent neural networks.

    Directory of Open Access Journals (Sweden)

    Jérémie Cabessa

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

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

    Directory of Open Access Journals (Sweden)

    Wensheng Guo

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

  17. 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.

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

    Directory of Open Access Journals (Sweden)

    Paul eMiller

    2013-05-01

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

  19. Mirror Fermat Calabi-Yau threefolds and Landau-Ginzburg black-hole attractors

    Science.gov (United States)

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

    2006-05-01

    We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the moduli space of such 4-dimensional compactifications, we always find two species of extremal black hole attractors, depending on the choice of the Sp(4,Z) symplectic charge vector, one 1/2-BPS (which is always stable, according to general results of special Kahler geometry) and one non-BPS. The latter turns out to be stable (local minimum of the ``effective black hole potential'' V_{BH}) for non-vanishing central charge, whereas it is unstable (saddle point of V_{BH}) for the case of vanishing central charge. This is to be compared to the large volume limit of one-modulus CY_{3}-compactifications (of Type II A superstrings), in which the homogeneous symmetric special Kahler geometry based on cubic prepotential admits (beside the 1/2-BPS ones) only non-BPS extremal black hole attractors with non-vanishing central charge, which are always stable.

  20. Control between coexistent attractors for optimal performance of a bistable piezoelectric vibration energy harvester

    Science.gov (United States)

    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.

  1. An attractor-based complexity measurement for Boolean recurrent neural networks.

    Science.gov (United States)

    Cabessa, Jérémie; Villa, Alessandro E P

    2014-01-01

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

  2. Using cell fate attractors to uncover transcriptional regulation of HL60 neutrophil differentiation

    Directory of Open Access Journals (Sweden)

    Kauffman Stuart A

    2009-02-01

    Full Text Available Abstract Background The process of cellular differentiation is governed by complex dynamical biomolecular networks consisting of a multitude of genes and their products acting in concert to determine a particular cell fate. Thus, a systems level view is necessary for understanding how a cell coordinates this process and for developing effective therapeutic strategies to treat diseases, such as cancer, in which differentiation plays a significant role. Theoretical considerations and recent experimental evidence support the view that cell fates are high dimensional attractor states of the underlying molecular networks. The temporal behavior of the network states progressing toward different cell fate attractors has the potential to elucidate the underlying molecular mechanisms governing differentiation. Results Using the HL60 multipotent promyelocytic leukemia cell line, we performed experiments that ultimately led to two different cell fate attractors by two treatments of varying dosage and duration of the differentiation agent all-trans-retinoic acid (ATRA. The dosage and duration combinations of the two treatments were chosen by means of flow cytometric measurements of CD11b, a well-known early differentiation marker, such that they generated two intermediate populations that were poised at the apparently same stage of differentiation. However, the population of one treatment proceeded toward the terminally differentiated neutrophil attractor while that of the other treatment reverted back toward the undifferentiated promyelocytic attractor. We monitored the gene expression changes in the two populations after their respective treatments over a period of five days and identified a set of genes that diverged in their expression, a subset of which promotes neutrophil differentiation while the other represses cell cycle progression. By employing promoter based transcription factor binding site analysis, we found enrichment in the set of divergent

  3. Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for k-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-Schr(o)dinger Equation

    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 .

  4. q-deformed statistical-mechanical property in the dynamics of trajectories en route to the Feigenbaum attractor.

    Science.gov (United States)

    Robledo, A; Moyano, L G

    2008-03-01

    We demonstrate that the dynamics toward and within the Feigenbaum attractor combine to form a q -deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is described by a q entropy obtained from a partition function generated by summing distances between neighboring positions of the attractor. The values of the q indices involved are given by the unimodal map universal constants, while the thermodynamic structure is closely related to that formerly developed for multifractals. As an essential component in our demonstration we expose, in great detail, the features of the dynamics of trajectories that either evolve toward the Feigenbaum attractor or are captured by its matching repellor. The dynamical properties of the family of periodic superstable cycles in unimodal maps are seen to be key ingredients for the comprehension of the discrete scale invariance features present at the period-doubling transition to chaos. Elements in our analysis are the following. (i) The preimages of the attractor and repellor of each of the supercycles appear entrenched into a fractal hierarchical structure of increasing complexity as period doubling develops. (ii) The limiting form of this rank structure results in an infinite number of families of well-defined phase-space gaps in the positions of the Feigenbaum attractor or of its repellor. (iii) The gaps in each of these families can be ordered with decreasing width in accordance with power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. (iv) The power law with log-periodic modulation associated with the rate of approach of trajectories toward the attractor (and to the repellor) is explained in terms of the progression of gap formation. (v) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated

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

    Directory of Open Access Journals (Sweden)

    Michael Alexander Nugent

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

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

    Science.gov (United States)

    Nugent, Michael Alexander; Molter, Timothy Wesley

    2014-01-01

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

  7. Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors

    Science.gov (United States)

    Barrio, Roberto; Blesa, Fernando; Serrano, Sergio

    2009-06-01

    In this paper we study different aspects of the paradigmatic Rössler model. We perform a detailed study of the local and global bifurcations of codimension one and two of limit cycles. This provides us a global idea of the three-parametric evolution of the system. We also study the regions of parameters where we may expect a chaotic behavior by the use of different Chaos Indicators. The combination of the different techniques gives an idea of the different routes to chaos and the different kinds of chaotic attractors we may found in this system.

  8. Audio-Visual Attractors for Capturing Attention to the Screens When Walking in CAVE Systems

    OpenAIRE

    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...

  9. Non-smooth saddle-node bifurcations III: Strange attractors in continuous time

    Science.gov (United States)

    Fuhrmann, G.

    2016-08-01

    Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a non-smooth bifurcation. By a previous result on the occurrence of non-smooth bifurcations in forced discrete time dynamical systems, this yields that within the class of families of quasiperiodically driven differential equations, non-smooth saddle-node bifurcations occur in a set with non-empty C2-interior.

  10. A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating

    Directory of Open Access Journals (Sweden)

    V.-T. Pham

    2014-11-01

    Full Text Available 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 control method is also designed and MATLAB simulations are shown. Finally, an electronic circuit emulating the memristor-based hyperchaotic system has been designed using off-the-shelf components.

  11. Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity

    CERN Document Server

    Dall'Agata, Gianguido

    2010-01-01

    We investigate the existence of supersymmetric static dyonic black holes with spherical horizon in the context of N= 2 U(1) gauged supergravity in four dimensions. We analyze the conditions for their existence and provide the general first-order flow equations driving the scalar fields and the metric warp factors from the asymptotic AdS4 geometry to the horizon. We work in a general duality-symmetric setup, which allows to describe both electric and magnetic gaugings. We also discuss the attractor mechanism and the issue of moduli (de-)stabilization.

  12. Waves attractors in rotating fluids a paradigm for ill-posed Cauchy problems

    CERN Document Server

    Rieutord, M; Valdettaro, L

    2000-01-01

    In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.

  13. Smooth attractors of finite dimension for von Karman evolutions with nonlinear frictional damping localized in a boundary layer

    CERN Document Server

    Geredeli, Pelin G; Webster, Justin T

    2012-01-01

    In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the long-time behavior of nonlinear plates has been a topic of recent interest. Since the von Karman plate system is of "hyperbolic type" with critical nonlinearity (noncompact with respect to the phase space), this latter topic is particularly challenging in the case of geometrically constrained and nonlinear damping. In this paper we first show the existence of a compact global attractor for finite-energy solutions, and we then prove that the attractor is both smooth and finite dimensional. Thus, the hyperbolic-like flow is stabilized asymptotically to a smooth and finite dimensional set. Key terms: dynamical systems, long-time behavior, global attractors, nonlinear plates, nonlinear damping, localized damping

  14. Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

    International Nuclear Information System (INIS)

    A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincaré maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system. (general)

  15. A source-attractor approach to network detection of radiation sources

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Qishi [University of Memphis; Barry, M. L.. [New Jersey Institute of Technology; Grieme, M. [New Jersey Institute of Technology; Sen, Satyabrata [ORNL; Rao, Nageswara S [ORNL; Brooks, Richard R [Clemson University

    2016-01-01

    Radiation source detection using a network of detectors is an active field of research for homeland security and defense applications. We propose Source-attractor Radiation Detection (SRD) method to aggregate measurements from a network of detectors for radiation source detection. SRD method models a potential radiation source as a magnet -like attractor that pulls in pre-computed virtual points from the detector locations. A detection decision is made if a sufficient level of attraction, quantified by the increase in the clustering of the shifted virtual points, is observed. Compared with traditional methods, SRD has the following advantages: i) it does not require an accurate estimate of the source location from limited and noise-corrupted sensor readings, unlike the localizationbased methods, and ii) its virtual point shifting and clustering calculation involve simple arithmetic operations based on the number of detectors, avoiding the high computational complexity of grid-based likelihood estimation methods. We evaluate its detection performance using canonical datasets from Domestic Nuclear Detection Office s (DNDO) Intelligence Radiation Sensors Systems (IRSS) tests. SRD achieves both lower false alarm rate and false negative rate compared to three existing algorithms for network source detection.

  16. Orbits and attractors for N=2 Maxwell-Einstein supergravity theories in five dimensions

    International Nuclear Information System (INIS)

    BPS and non-BPS orbits for extremal black-holes in N=2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions were classified long ago by the present authors for the case of symmetric scalar manifolds. Motivated by these results and some recent work on non-supersymmetric attractors we show that attractor equations in N=2 MESGTs in d=5 do indeed possess the distinct families of solutions with finite Bekenstein-Hawking entropy. The new non-BPS solutions have non-vanishing central charge and matter charge which is invariant under the maximal compact subgroup K-bar of the stabilizer H-bar of the non-BPS orbit. Our analysis covers all symmetric space theories G/H such that G is a symmetry of the action. These theories are in one-to-one correspondence with (Euclidean) Jordan algebras of degree three. In the particular case of N=2 MESGT with scalar manifold SU*(6)/USp(6) a duality of the two solutions with regard to N=2 and N=6 supergravity is also considered

  17. Determining a singleton attractor of a boolean network with nested canalyzing functions.

    Science.gov (United States)

    Akutsu, Tatsuya; Melkman, Avraham A; Tamura, Takeyuki; Yamamoto, Masaki

    2011-10-01

    In this article, we study the problem of finding a singleton attractor for several biologically important subclasses of Boolean networks (BNs). The problem of finding a singleton attractor in a BN is known to be NP-hard in general. For BNs consisting of n nested canalyzing functions, we present an O(1.799(n)) time algorithm. The core part of this development is an O(min(2(k/2) · 2(m/2), 2(k)) · poly(k, m)) time algorithm for the satisfiability problem for m nested canalyzing functions over k variables. For BNs consisting of chain functions, a subclass of nested canalyzing functions, we present an O(1.619(n)) time algorithm and show that the problem remains NP-hard, even though the satisfiability problem for m chain functions over k variables is solvable in polynomial time. Finally, we present an o(2(n)) time algorithm for bounded degree BNs consisting of canalyzing functions.

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

    Science.gov (United States)

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

    2012-04-01

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

  19. Rohlin distance and the evolution of influenza A virus: weak attractors and precursors.

    Directory of Open Access Journals (Sweden)

    Raffaella Burioni

    Full Text Available The evolution of the hemagglutinin amino acids sequences of Influenza A virus is studied by a method based on an informational metrics, originally introduced by Rohlin for partitions in abstract probability spaces. This metrics does not require any previous functional or syntactic knowledge about the sequences and it is sensitive to the correlated variations in the characters disposition. Its efficiency is improved by algorithmic tools, designed to enhance the detection of the novelty and to reduce the noise of useless mutations. We focus on the USA data from 1993/94 to 2010/2011 for A/H3N2 and on USA data from 2006/07 to 2010/2011 for A/H1N1. We show that the clusterization of the distance matrix gives strong evidence to a structure of domains in the sequence space, acting as weak attractors for the evolution, in very good agreement with the epidemiological history of the virus. The structure proves very robust with respect to the variations of the clusterization parameters, and extremely coherent when restricting the observation window. The results suggest an efficient strategy in the vaccine forecast, based on the presence of "precursors" (or "buds" populating the most recent attractor.

  20. A Strange Double-Deck Butterfly Chaotic Attractor from a Permanent Magnet Synchronous Motor with Smooth Air Gap: Numerical Analysis and Experimental Observation

    Directory of Open Access Journals (Sweden)

    Zhonglin Wang

    2014-01-01

    Full Text Available A permanent magnet synchronous motor (PMSM model with smooth air gap and an exogenous periodic input is introduced and analyzed in this paper. With a simple mathematical transformation, a new nonautonomous Lorenz-like system is derived from this PMSM model, and this new three-dimensional system can display the complicated dynamics such as the chaotic attractor and the multiperiodic orbits by adjusting the frequency and amplitude of the exogenous periodic inputs. Moreover, this new system shows a double-deck chaotic attractor that is completely different from the four-wing chaotic attractors on topological structures, although the phase portrait shapes of the new attractor and the four-wing chaotic attractors are similar. The exotic phenomenon has been well demonstrated and investigated by numerical simulations, bifurcation analysis, and electronic circuit implementation.

  1. Charge density study with the Maximum Entropy Method on model data of silicon. A search for non-nuclear attractors

    NARCIS (Netherlands)

    Vries, de R.Y.; Briels, W.J.; Feil, D.; Velde, te G.; Baerends, E.J.

    1996-01-01

    1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of

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

    Science.gov (United States)

    Park, Jeryang; Rao, P. Suresh C.

    2014-11-01

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

  3. The Global Attractor of a Non-Local PDE Model with Delay for Population Dynamics in Rn

    Institute of Scientific and Technical Information of China (English)

    Zhi Xiang LI

    2011-01-01

    In this paper, we consider a non-local PDE model with delay for population dynamics in R. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup.

  4. Bounds on the attractor dimension for magnetohydrodynamic channel flow with parallel magnetic field at low magnetic Reynolds number.

    Science.gov (United States)

    Low, R; Pothérat, A

    2015-05-01

    We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well adapted to the problem of finding the attractor dimension and which is also used in subsequent direct numerical simulation of these flows. For given Reynolds and Hartmann numbers, we obtain an upper bound for the dimension of the attractor by means of known bounds on the nonlinear inertial term and this functional basis for the flow. Three distinct flow regimes emerge: a quasi-isotropic three-dimensional (3D) flow, a nonisotropic 3D flow, and a 2D flow. We find the transition curves between these regimes in the space parametrized by Hartmann number Ha and attractor dimension d(att). We find how the attractor dimension scales as a function of Reynolds and Hartmann numbers (Re and Ha) in each regime. We also investigate the thickness of the boundary layer along the bounding wall and find that in all regimes this scales as 1/Re, independently of the value of Ha, unlike Hartmann boundary layers found when the field is normal to the channel. The structure of the set of least dissipative modes is indeed quite different between these two cases but the properties of turbulence far from the walls (smallest scales and number of degrees of freedom) are found to be very similar.

  5. Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models

    CERN Document Server

    Rajpoot, Subhash

    2016-01-01

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

  6. Bounds on the attractor dimension for magnetohydrodynamic channel flow with parallel magnetic field at low magnetic Reynolds number.

    Science.gov (United States)

    Low, R; Pothérat, A

    2015-05-01

    We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well adapted to the problem of finding the attractor dimension and which is also used in subsequent direct numerical simulation of these flows. For given Reynolds and Hartmann numbers, we obtain an upper bound for the dimension of the attractor by means of known bounds on the nonlinear inertial term and this functional basis for the flow. Three distinct flow regimes emerge: a quasi-isotropic three-dimensional (3D) flow, a nonisotropic 3D flow, and a 2D flow. We find the transition curves between these regimes in the space parametrized by Hartmann number Ha and attractor dimension d(att). We find how the attractor dimension scales as a function of Reynolds and Hartmann numbers (Re and Ha) in each regime. We also investigate the thickness of the boundary layer along the bounding wall and find that in all regimes this scales as 1/Re, independently of the value of Ha, unlike Hartmann boundary layers found when the field is normal to the channel. The structure of the set of least dissipative modes is indeed quite different between these two cases but the properties of turbulence far from the walls (smallest scales and number of degrees of freedom) are found to be very similar. PMID:26066263

  7. Late time accelerated scaling attractors in DGP (Dvali-Gabadadze-Porrati) braneworld

    CERN Document Server

    Dutta, Jibitesh; Syiemlieh, Erickson

    2016-01-01

    In the evolution of late universe, the main source of matter are Dark energy and Dark matter. They are indirectly detected only through their gravitational manifestations. So the possibility of interaction with each other without violating observational restrictions is not ruled out. With this motivation, we investigate the dynamics of DGP braneworld where source of dark energy is a scalar field and it interacts with matter source. Since observation favours phantom case more, we have also studied the dynamics of interacting phantom scalar field. In non interacting DGP braneworld there are no late time accelerated scaling attractors and hence cannot alleviate Coincidence problem. In this paper, we shall show that it is possible to get late time accelerated scaling solutions. The phase space is studied by taking two categories of potentials (Exponential and Non exponential functions). The stability of critical points are examined by taking two specific interactions. The first interaction gives late time acceler...

  8. Structure of Kaehler potential for D-term inflationary attractor models

    Energy Technology Data Exchange (ETDEWEB)

    Nakayama, Kazunori [Tokyo Univ. (Japan). Dept. of Physics; Tokyo Univ., Chiba (Japan). Kavli IPMU (WPI), UTIAS; Saikawa, Ken' ichi [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Tokyo Institute of Technology (Japan). Dept. of Physics; Terada, Takahiro [Tokyo Univ. (Japan). Dept. of Physics; Asia Pacific Center for Theoretical Physics (APCTP), Pohang (Korea, Republic of); Yamaguchi, Masahide [Tokyo Institute of Technology (Japan). Dept. of Physics

    2016-05-15

    Minimal chaotic models of D-term inflation predicts too large primordial tensor perturbations. Although it can be made consistent with observations utilizing higher order terms in the Kaehler potential, expansion is not controlled in the absence of symmetries. We comprehensively study the conditions of Kaehler potential for D-term plateau-type potentials and discuss its symmetry. They include the α-attractor model with a massive vector supermultiplet and its generalization leading to pole inflation of arbitrary order. We extend the models so that it can describe Coulomb phase, gauge anomaly is cancelled, and fields other than inflaton are stabilized during inflation. We also point out a generic issue for large-field D-term inflation that the masses of the non-inflaton fields tend to exceed the Planck scale.

  9. The effect of non-equilibrium conditions and filtering on the dimension of the Lorenz attractor

    International Nuclear Information System (INIS)

    A chaotic system is modeled under typical experimental conditions and the effect on the correlation dimension is examined. Numerical data from the Lorenz attractor are used in which one of the parameters is varied in time, representing a non-equilibrium condition. The Lorenz time series is also filtered using a digital low-pass filter algorithm. An increase in the dimension is seen for a sinusoidal variation dependent on the amplitude of the perturbation. A linear variation yields no consistent results. Moderate filtering leads to a slight increase in dimension, with the occasional emergence of a spurious second plateau. Stronger filtering suppresses both plateaus, and no dimension can be assigned. The implications of the results on experimental data analysis are discussed. 12 refs., 9 figs., 5 tabs

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

    Science.gov (United States)

    Cao, Hongduo; Li, Ying

    2014-03-01

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

  11. A quantitative measure, mechanism and attractor for self-organization in networked complex systems

    CERN Document Server

    Georgiev, Georgi Yordanov

    2012-01-01

    Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck's constant. The meaning of quantity of organization is the inverse of the number of quanta of action per one unit motion of an element. This definition can be applied to the organization of any complex system. Systems self-organize to decrease the average action per element per unit motion. This lowest action state is the attractor for the continuous self-organization and evolution of a dynamical complex system. Constraints increase this average action and constraint minimization by the elements is a basic mechanism for action minimization. Increase of quantity of elements in a network, leads to faster constraint minimization through grouping, decrease of average action per element and motion and therefore accelerated rate of self-organization. Progressive development, as self-organization, is a process of minimization of action.

  12. Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

    Institute of Scientific and Technical Information of China (English)

    Varga K.KALANTAROV; Edriss S.TITI

    2009-01-01

    The authors investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous (inviscid) regulaxization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes-Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient ν→ 0.

  13. Global attractor of coupled difference equations and applications to Lotka-Volterra systems

    Directory of Open Access Journals (Sweden)

    Pao CV

    2005-01-01

    Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.

  14. Global attractor of coupled difference equations and applications to Lotka-Volterra systems

    Directory of Open Access Journals (Sweden)

    C. V. Pao

    2005-03-01

    Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.

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

    International Nuclear Information System (INIS)

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

  16. Strong global attractor for a quasilinear nonlocal wave equation on $mathbb{R}^N$

    Directory of Open Access Journals (Sweden)

    Perikles G. Papadopoulos

    2006-07-01

    Full Text Available We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation $$ u_{tt}-phi (x| abla u(t|^{2}Delta u+delta u_{t}+|u|^{a}u=0, $$ in $mathbb{R}^N$, $t geq 0$, with initial conditions $ u(x,0 = u_0 (x$ and $u_t(x,0 = u_1(x$. We consider the case $N geq 3$, $delta> 0$, and $(phi (x^{-1}$ a positive function in $L^{N/2}(mathbb{R}^Ncap L^{infty}(mathbb{R}^N $. The existence of a global attractor is proved in the strong topology of the space $mathcal{D}^{1,2}(mathbb{R}^N imes L^{2}_{g}(mathbb{R}^N$.

  17. d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms

    CERN Document Server

    Bellucci, S; Marrani, A; Yeranyan, A

    2008-01-01

    We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d>4, as well. Thence, we work out the example of the stu model of N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and D0-D6 BH charge configurations, and in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and SO(8)-truncated ones. The attractive nature of the critical points, related to the semi-positive definiteness of the Hessian matrix, is also studied.

  18. Strange non-chaotic attractors in quasiperiodically forced circle maps: Diophantine forcing

    CERN Document Server

    Jäger, T

    2011-01-01

    We study parameter families of quasiperiodically forced (qpf) circle maps with Diophantine frequency. Under certain C1-open conditions concerning their geometry, we prove that these families exhibit nonuniformly hyperbolic behaviour, often referred to as the existence of strange nonchaotic attractors, on parameter sets of positive measure. This provides a nonlinear version of results by Young on quasiperiodic SL (2;R)-cocycles and complements previous results in this direction which hold for sets of frequencies of positive measure, but did not allow for an explicit characterisation of these frequencies. As an application, we study a qpf version of the Arnold circle map and show that the Arnold tongue corresponding to rotation number 1/2 collapses on an open set of parameters. The proof requires to perform a parameter exclusion with respect to some twist parameter and is based on the multiscale analysis of the dynamics on certain dynamically defined critical sets. A crucial ingredient is to obtain good control...

  19. BOUNDARY CRISIS OF ATTRACTOR IN THE SIMULATION CAUSES OF THE DEGRADATION OF COMMERCIAL BIORESOURCES

    Directory of Open Access Journals (Sweden)

    A. Yu. Perevarukha

    2015-01-01

    Full Text Available The article describes the computational model that unites the formalization of ecological features of the reproductive cycle of anadromous fish and the possibility of studying nonlinear effects in the population dynamics under anthropogenic impact. Event-driven component implemented in continuous time has allowed us to take into account changes in the survival generation in interrelation with the factors of growth rate. Discrete component trajectory of the dynamical system has two areas of attraction and is characterized by the reverse tangent bifurcation due to the impact of fishing, which dramatically transforms the population with the condition of irregular fluctuations in low numbers. The further emergence of «boundary crisis» for the interval attractor describes a common scenario an irreversible degradation of biological resources.

  20. Statistics of the stochastically-forced Lorenz attractor by the Fokker-Planck and cumulant equations

    CERN Document Server

    Allawala, Altan

    2016-01-01

    We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz-63 attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator using linear algebra. Two variants are also studied: A self-adjoint construction of the linear operator, and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. Comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed.

  1. Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses

    International Nuclear Information System (INIS)

    By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dxij/dt=-aijxij-ΣCkl(set-membershipsign)Nr(i,j)Cijklfij[xkl(t)]xij+Lij(t), t>0,t≠tk; Δxij(tk)=xij(tk+)-xij(tk-)=Ik[xij(tk)], k=1,2,... . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.

  2. Structured patterns retrieval using a metric attractor network: Application to fingerprint recognition

    Science.gov (United States)

    Doria, Felipe; Erichsen, Rubem; González, Mario; Rodríguez, Francisco B.; Sánchez, Ángel; Dominguez, David

    2016-09-01

    The ability of a metric attractor neural networks (MANN) to learn structured patterns is analyzed. In particular we consider collections of fingerprints, which present some local features, rather than being modeled by random patterns. The network retrieval proved to be robust to varying the pattern activity, the threshold strategy, the topological arrangement of the connections, and for several types of noisy configuration. We found that the lower the fingerprint patterns activity is, the higher the load ratio and retrieval quality are. A simplified theoretical framework, for the unbiased case, is developed as a function of five parameters: the load ratio, the finiteness connectivity, the density degree of the network, randomness ratio, and the spatial pattern correlation. Linked to the latter appears a new neural dynamics variable: the spatial neural correlation. The theory agrees quite well with the experimental results.

  3. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Danxia Wang

    2015-01-01

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

  4. Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay

    Science.gov (United States)

    Zhusubaliyev, Z. T.; Mosekilde, E.; Churilov, A. N.; Medvedev, A.

    2015-07-01

    The release of luteinizing hormone (LH) is driven by intermittent bursts of activity in the hypothalamic nerve centers of the brain. Luteinizing hormone again stimulates release of the male sex hormone testosterone (Te) and, via the circulating concentration of Te, the hypothalamic nerve centers are subject to a negative feedback regulation that is capable of modifying the intermittent bursts into more regular pulse trains. Bifurcation analysis of a hybrid model that attempts to integrate the intermittent bursting activity with a continuous hormone secretion has recently demonstrated a number of interesting nonlinear dynamic phenomena, including bistability and deterministic chaos. The present paper focuses on the additional complexity that arises when the time delay in the continuous part of the model exceeds the typical bursting interval of the feedback. Under these conditions, the hybrid model is capable of displaying quasiperiodicity and border collisions as well as multistability and hidden attractors.

  5. Internal wave attractors examined using laboratory experiments and 3D numerical simulations

    CERN Document Server

    Brouzet, Christophe; Scolan, H; Ermanyuk, E V; Dauxois, Thierry

    2016-01-01

    In the present paper, we combine numerical and experimental approaches to study the dynamics of stable and unstable internal wave attractors. The problem is considered in a classic trapezoidal setup filled with a uniformly stratified fluid. Energy is injected into the system at global scale by the small-amplitude motion of a vertical wall. Wave motion in the test tank is measured with the help of conventional synthetic schlieren and PIV techniques. The numerical setup closely reproduces the experimental one in terms of geometry and the operational range of the Reynolds and Schmidt numbers. The spectral element method is used as a numerical tool to simulate the nonlinear dynamics of a viscous salt-stratified fluid. We show that the results of three-dimensional calculations are in excellent qualitative and quantitative agreement with the experimental data, including the spatial and temporal parameters of the secondary waves produced by triadic resonance instability. Further, we explore experimentally and numeri...

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

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    Laura Dempere-Marco

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

  7. In-in and δN calculations of the bispectrum from non-attractor single-field inflation

    Science.gov (United States)

    Chen, Xingang; Firouzjahi, Hassan; Komatsu, Eiichiro; Namjoo, Mohammad Hossein; Sasaki, Misao

    2013-12-01

    In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as Script Rproptoa3. This is so far the only known class of self-consistent single-field models with a Bunch-Davies initial state that can produce a large squeezed-limit bispectrum violating Maldacena's consistency relation. Given the importance of this result, we calculate the bispectrum with three different methods: using quantum field theory calculations in two different gauges, and classical calculations (the δN formalism). All the results agree, giving the local-form bispectrum parameter of flocalNL = 5(1+cs2)/(4cs2). This result is valid for arbitrary values of the speed of sound parameter, cs, for a particular non-attractor model we consider in this paper.

  8. Random attractors in $H^1$ for stochastic two dimensional micropolar fluid flows with spatial-valued noises

    Directory of Open Access Journals (Sweden)

    Wenqiang Zhao

    2014-11-01

    Full Text Available This work studies the long-time behavior of two-dimensional micropolar fluid flows perturbed by the generalized time derivative of the infinite dimensional Wiener processes. Based on the omega-limit compactness argument as well as some new estimates of solutions, it is proved that the generated random dynamical system admits an H^1-random attractor which is compact in H^1 space and attracts all tempered random subsets of L^2 space in H^1 topology. We also give a general abstract result which shows that the continuity condition and absorption of the associated random dynamical system in H^1 space is not necessary for the existence of random attractor in H^1 space.

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

    Science.gov (United States)

    Simpson, D. J. W.

    2016-09-01

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

  10. Inertial Wave Excitation and Wave Attractors in an Annular Tank: DNS

    Science.gov (United States)

    Klein, Marten; Ghasemi, Abouzar; Harlander, Uwe; Will, Andreas

    2014-05-01

    Rotation is the most relevant aspect of geophysical fluid dynamics, manifesting itself by the Coriolis force. Small perturbations to the state of rigid body rotation can excite inertial waves (waves restored by Coriolis force) with frequencies in the range 0 fluid so that inertial waves remain the only waves in the mathematical model, which can transport kinetic energy and angular momentum. In geophysics, inertial waves have received a lot attention over the last decades. A spherical shell, for instance, is already non-simple in a sense that its inertial mode's spatial structures are complex, forming so-called wave attractors [1]. But also other containers have been investigated, e.g., cylinders and boxes from the viewpoints of normal mode excitation [2,3], mean flow generation and boundary layer flow [4]. A simple wave attractor was found in a prism, which can be seen as idealized ocean basin [5]. However, local mechanisms of wave excitation are still not very well understood. In order to contribute to the ongoing discussion, we consider an annular geometry. Its rectangular symmetry was broken by replacing the inner cylinder with a frustum of apex half-angle α = 5.7°. The annular gap is filled with a fluid of kinematic viscosity ν. The whole vessel rotates with a mean angular velocity Ω0 around its axis of symmetry. Ekman numbers investigated are 1 ≠« E = ν(Ω0H2)-1 ≥ 10-5. Similarly to [1-5] we perturb the system by longitudinal libration, Ω(t) = Ω0(1 + ɛsinωt), where ω > 0 denotes the frequency and 0 Fluids (2012), vol. 24, 076602. [3] A. Sauret, D. Cébron, M. Le Bars and S. Le Dizès, Phys. Fluids (2012), vol. 24, 026603. [4] F. H. Busse, Physica D, vol. 240 (2011), pp. 208-211. [5] L. R. M. Maas, J. Fluid Mech. (2001), vol. 437, pp. 13-28.

  11. Chaos-Geometric approach to analysis of chaotic attractor dynamics for the one-ring fibre laser

    Directory of Open Access Journals (Sweden)

    Georgy Prepelitsa

    2015-09-01

    Full Text Available Earlier we have developed new chaos-geometric approach to  modelling and analysis of nonlinear processes dynamics of the complex systems. It combines together application of the advanced mutual information approach, correlation integral analysis, Lyapunov exponent's analysis etc. Here we present the results of its application to studying low-and high-D attractor dynamics of the one-ring fibre laser

  12. Pullback attractors of the two-dimensional non-autonomous simplified Ericksen-Leslie system for nematic liquid crystal flows

    Science.gov (United States)

    You, Bo; Li, Fang

    2016-08-01

    This paper is concerned with the long-time behaviour of the two-dimensional non-autonomous simplified Ericksen-Leslie system for nematic liquid crystal flows introduced in Lin and Liu (Commun Pure Appl Math, 48:501-537, 1995) with a non-autonomous forcing bulk term and order parameter field boundary conditions. In this paper, we prove the existence of pullback attractors and estimate the upper bound of its fractal dimension under some suitable assumptions.

  13. The role of the positive emotional attractor in vision and shared vision: toward effective leadership, relationships, and engagement.

    Science.gov (United States)

    Boyatzis, Richard E; Rochford, Kylie; Taylor, Scott N

    2015-01-01

    Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA) and the negative emotional attractor (NEA). These two primary states are strange attractors, each characterized by three dimensions: (1) positive versus negative emotional arousal; (2) endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3) neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one's purpose and ideal self). We begin our paper by reviewing the underpinnings of our PEA-NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory. PMID:26052300

  14. The Role of the Positive and Negative Emotional Attractors in Vision and Shared Vision: Toward Effective Leadership, Relationships and Engagement

    Directory of Open Access Journals (Sweden)

    Richard Eleftherios Boyatzis

    2015-05-01

    Full Text Available Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA and the negative emotional attractor (NEA. These two primary states are strange attractors, each characterized by three dimensions: (1 positive versus negative emotional arousal; (2 endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3 neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one’s purpose and ideal self. We begin our paper by reviewing the underpinnings of our PEA-NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory.

  15. Pathway Analysis Based on Attractor and Cross Talk in Colon Cancer

    Directory of Open Access Journals (Sweden)

    Yanxia Liu

    2016-01-01

    Full Text Available Colon cancer is the third and second most common cancer form in men and women worldwide. It is generally accepted that colon cancer mainly results from diet. The aim of this study was to identify core pathways which elucidated the molecular mechanisms in colon cancer. The microarray data of E-GEOD-44861 was downloaded from ArrayExpress database. All human pathways were obtained from Kyoto Encyclopedia of Genes and Genomes database. In total, 135 differential expressed genes (DEG were identified using Linear Models for Microarray Data package. Differential pathways were identified with the method of attractor after overlapping with DEG. Pathway cross talk network (PCN was constructed by combining protein-protein interactions and differential pathways. Cross talks of all pathways were obtained in PCN. There were 65 pathways with RankProd (RP values 100. Five pathways were satisfied with P value 100, which were considered to be the most important pathways in colon cancer. In conclusion, the five pathways were identified in the center status of colon cancer, which may contribute to understanding the mechanism and development of colon cancer.

  16. Vestibular and Attractor Network Basis of the Head Direction Cell Signal in Subcortical Circuits

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    Benjamin J Clark

    2012-03-01

    Full Text Available Accurate navigation depends on a network of neural systems that encode the moment-to-moment changes in an animal’s directional orientation and location in space. Within this navigation system are head direction (HD cells, which fire persistently when an animal’s head is pointed in a particular direction (Sharp et al., 2001a; Taube, 2007. HD cells are widely thought to underlie an animal’s sense of spatial orientation, and research over the last 25+ years has revealed that this robust spatial signal is widely distributed across subcortical and cortical limbic areas. Much of this work has been directed at understanding the functional organization of the HD cell circuitry, and precisely how this signal is generated from sensory and motor systems. The purpose of the present review is to summarize some of the recent studies arguing that the HD cell circuit is largely processed in a hierarchical fashion, following a pathway involving the dorsal tegmental nuclei → lateral mammillary nuclei → anterior thalamus → parahippocampal and retrosplenial cortical regions. We also review recent work identifying bursting cellular activity in the HD cell circuit after lesions of the vestibular system, and relate these observations to the long held view that attractor network mechanisms underlie HD signal generation. Finally, we summarize the work to date suggesting that this network architecture may reside within the tegmento-mammillary circuit.

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

    Science.gov (United States)

    Reuveni, Eli; Giuliani, Alessandro

    2012-02-01

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

  18. The Mass Distribution of the Great Attractor as Revealed by a Deep NIR Survey

    CERN Document Server

    Kraan-Korteweg, R C; Woudt, P A; Nagayama, T; Wakamatsu, K

    2011-01-01

    This paper presents the analysis of a deep near-infrared J,H,Ks-imaging survey (37.5 sq deg) aimed at tracing the galaxy distribution of the Great Attractor (GA) in the Zone of Avoidance along the so-called Norma Wall. The resulting galaxy catalog is complete to extinction-corrected magnitudes Ks^o = 14.8 mag for extinctions less than A_K = 1.0 mag and star densities below log N(Ks<14.0) < 4.72. Of the 4360 cataloged galaxies, 99.2% lie in the hereby constrained 89.5% of the survey area. Although the analyzed galaxy distribution reveals no new major galaxy clusters at the GA distance (albeit some more distant ones), the overall number counts and luminosity density indicate a clear and surprisingly smooth overdensity at the GA distance that extends over the whole surveyed region. A mass estimate of the Norma Wall overdensity derived from (a) galaxy number counts and (b) photometric redshift distribution gives a lower value compared to the original prediction by Lynden-Bell et al. 1988 (~14%), but is cons...

  19. Study of the attractor structure of an agent-based sociological model

    International Nuclear Information System (INIS)

    The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabasi-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.

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

    CERN Document Server

    Ferrara, Sergio

    2016-01-01

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

  1. Some Convex Functions Based Measures of Independence and Their Application to Strange Attractor Reconstruction

    Directory of Open Access Journals (Sweden)

    Kazuyuki Aihara

    2011-04-01

    Full Text Available The classical information-theoretic measures such as the entropy and the mutual information (MI are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO and the quasientropy (QE as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI. A quality factor (QF is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.

  2. Hierarchy, dimension, attractor and self-organization -- dynamics of mode-locked fiber lasers

    CERN Document Server

    Wei, Huai; Shi, Wei; Zhu, Xiushan; Norwood, Robert A; Peyghambarian, Nasser; Jian, Shuisheng

    2016-01-01

    Mode-locked fiber lasers are one of the most important sources of ultra-short pulses. However, A unified description for the rich variety of states and the driving forces behind the complex and diverse nonlinear behavior of mode-locked fiber lasers have yet to be developed. Here we present a comprehensive theoretical framework based upon complexity science, thereby offering a fundamentally new way of thinking about the behavior of mode-locked fiber lasers. This hierarchically structured frame work provide a model with and changeable variable dimensionality resulting in a simple and elegant view, with which numerous complex states can be described systematically. The existence of a set of new mode-locked fiber laser states is proposed for the first time. Moreover, research into the attractors' basins reveals the origin of stochasticity, hysteresis and multistability in these systems. These findings pave the way for dynamics analysis and new system designs of mode-locked fiber lasers. The paradigm will have a w...

  3. FAST MOTIONS OF GALAXIES IN THE COMA I CLOUD: A CASE OF DARK ATTRACTOR?

    International Nuclear Information System (INIS)

    We note that nearby galaxies having high negative peculiar velocities are distributed over the sky very inhomogeneously. A part of this anisotropy is caused by the 'Local Velocity Anomaly', i.e., by the bulk motion of nearby galaxies away from the Local Void. However, half of the fast-flying objects reside within a small region known as the Coma I cloud. According to Makarov and Karachentsev, this complex contains 8 groups, 5 triplets, 10 pairs, and 83 single galaxies with a total mass of 4.7 × 1013 M☉. We use 122 galaxies in the Coma I region with known distances and radial velocities VLG –1 to draw the Hubble relation for them. The Hubble diagram shows a Z-shaped effect of infall with an amplitude of +200 km s–1 on the nearby side and –700 km s–1 on the back side. This phenomenon can be understood as the galaxy infall toward a dark attractor with a mass of ∼2 × 1014 M☉ situated at a distance of 15 Mpc from us. The existence of a large void between the Coma and Virgo clusters also probably affects the Hubble flow around the Coma I.

  4. Pathway Analysis Based on Attractor and Cross Talk in Colon Cancer

    Science.gov (United States)

    2016-01-01

    Colon cancer is the third and second most common cancer form in men and women worldwide. It is generally accepted that colon cancer mainly results from diet. The aim of this study was to identify core pathways which elucidated the molecular mechanisms in colon cancer. The microarray data of E-GEOD-44861 was downloaded from ArrayExpress database. All human pathways were obtained from Kyoto Encyclopedia of Genes and Genomes database. In total, 135 differential expressed genes (DEG) were identified using Linear Models for Microarray Data package. Differential pathways were identified with the method of attractor after overlapping with DEG. Pathway cross talk network (PCN) was constructed by combining protein-protein interactions and differential pathways. Cross talks of all pathways were obtained in PCN. There were 65 pathways with RankProd (RP) values 100. Five pathways were satisfied with P value 100, which were considered to be the most important pathways in colon cancer. In conclusion, the five pathways were identified in the center status of colon cancer, which may contribute to understanding the mechanism and development of colon cancer. PMID:27746583

  5. Hebbian Plasticity Realigns Grid Cell Activity with External Sensory Cues in Continuous Attractor Models.

    Science.gov (United States)

    Mulas, Marcello; Waniek, Nicolai; Conradt, Jörg

    2016-01-01

    After the discovery of grid cells, which are an essential component to understand how the mammalian brain encodes spatial information, three main classes of computational models were proposed in order to explain their working principles. Amongst them, the one based on continuous attractor networks (CAN), is promising in terms of biological plausibility and suitable for robotic applications. However, in its current formulation, it is unable to reproduce important electrophysiological findings and cannot be used to perform path integration for long periods of time. In fact, in absence of an appropriate resetting mechanism, the accumulation of errors over time due to the noise intrinsic in velocity estimation and neural computation prevents CAN models to reproduce stable spatial grid patterns. In this paper, we propose an extension of the CAN model using Hebbian plasticity to anchor grid cell activity to environmental landmarks. To validate our approach we used as input to the neural simulations both artificial data and real data recorded from a robotic setup. The additional neural mechanism can not only anchor grid patterns to external sensory cues but also recall grid patterns generated in previously explored environments. These results might be instrumental for next generation bio-inspired robotic navigation algorithms that take advantage of neural computation in order to cope with complex and dynamic environments. PMID:26924979

  6. Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems

    Science.gov (United States)

    Gentile, Guido; Bartuccelli, Michele V.; Deane, Jonathan H. B.

    2006-07-01

    We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasiperiodic forcing term and in the presence of damping. In the limit of large damping, under some generic nondegeneracy condition on the force, there are quasiperiodic solutions which have the same frequency vector as the forcing term. We prove that such solutions are Borel summable at the origin when the frequency vector is either any one-dimensional number or a two-dimensional vector such that the ratio of its components is an irrational number of constant type. In the first case the proof given simplifies that provided in a previous work of ours. We also show that in any dimension d, for the existence of a quasiperiodic solution with the same frequency vector as the forcing term, the standard Diophantine condition can be weakened into the Bryuno condition. In all cases, under a suitable positivity condition, the quasiperiodic solution is proved to describe a local attractor.

  7. Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles

    CERN Document Server

    Mitsui, Takahito; Aihara, Kazuyuki

    2015-01-01

    Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\\sim $40 kyr before the so-called middle Pleistocene transition between $\\sim$1.2 and $\\sim$0.7 Myr ago, and it is $\\sim $100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaoti...

  8. A model combining oscillations and attractor dynamics for generation of grid cell firing

    Directory of Open Access Journals (Sweden)

    Michael E Hasselmo

    2012-05-01

    Full Text Available 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 are termed heading angle cells because their connectivity depends upon heading angle in the environment as well as the spatial phase coded by the cell. These cells project to a population of grid cells. The sum of the heading angle input results in standing waves of circularly symmetric input to the grid cell population. Feedback from the grid cell population increases the activity of subsets of the heading angle cells, resulting in the network settling into activity patterns that resemble the patterns of firing fields in a population of grid cells. The properties of heading angle cells firing as conjunctive grid-by-head-direction cells can shift the grid cell firing according to movement velocity. The pattern of interaction of oscillations requires use of separate populations that fire on alternate cycles of the net theta rhythmic input to grid cells, similar to recent neurophysiological data on theta cycle skipping in medial entorhinal cortex.

  9. Local community detection as pattern restoration by attractor dynamics of recurrent neural networks.

    Science.gov (United States)

    Okamoto, Hiroshi

    2016-08-01

    Densely connected parts in networks are referred to as "communities". Community structure is a hallmark of a variety of real-world networks. Individual communities in networks form functional modules of complex systems described by networks. Therefore, finding communities in networks is essential to approaching and understanding complex systems described by networks. In fact, network science has made a great deal of effort to develop effective and efficient methods for detecting communities in networks. Here we put forward a type of community detection, which has been little examined so far but will be practically useful. Suppose that we are given a set of source nodes that includes some (but not all) of "true" members of a particular community; suppose also that the set includes some nodes that are not the members of this community (i.e., "false" members of the community). We propose to detect the community from this "imperfect" and "inaccurate" set of source nodes using attractor dynamics of recurrent neural networks. Community detection by the proposed method can be viewed as restoration of the original pattern from a deteriorated pattern, which is analogous to cue-triggered recall of short-term memory in the brain. We demonstrate the effectiveness of the proposed method using synthetic networks and real social networks for which correct communities are known.

  10. Noise in attractor networks in the brain produced by graded firing rate representations.

    Directory of Open Access Journals (Sweden)

    Tristan J Webb

    Full Text Available Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry.

  11. Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System

    Science.gov (United States)

    Li, Chun-Lai; Li, Wen; Zhang, Jing; Xie, Yuan-Xi; Zhao, Yi-Bo

    2016-09-01

    A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincaré map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. Supported by Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ4036, University Natural Science Foundation of Jiangsu Province under Grant No. 14KJB120007 and the National Natural Science Foundation of China under Grant Nos. 11504176 and 11602084

  12. Predicting pancreas cell fate decisions and reprogramming with a hierarchical multi-attractor model.

    Directory of Open Access Journals (Sweden)

    Joseph Xu Zhou

    Full Text Available Cell fate reprogramming, such as the generation of insulin-producing β cells from other pancreas cells, can be achieved by external modulation of key transcription factors. However, the known gene regulatory interactions that form a complex network with multiple feedback loops make it increasingly difficult to design the cell reprogramming scheme because the linear regulatory pathways as schemes of causal influences upon cell lineages are inadequate for predicting the effect of transcriptional perturbation. However, sufficient information on regulatory networks is usually not available for detailed formal models. Here we demonstrate that by using the qualitatively described regulatory interactions as the basis for a coarse-grained dynamical ODE (ordinary differential equation based model, it is possible to recapitulate the observed attractors of the exocrine and β, δ, α endocrine cells and to predict which gene perturbation can result in desired lineage reprogramming. Our model indicates that the constraints imposed by the incompletely elucidated regulatory network architecture suffice to build a predictive model for making informed decisions in choosing the set of transcription factors that need to be modulated for fate reprogramming.

  13. 多值半流的吸引子在随机扰动下的上半连续性%Upper semi-continuity of attractors for multivalued semi-flow under random perturbation

    Institute of Scientific and Technical Information of China (English)

    李挺; 刘曾荣

    2006-01-01

    In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered, then it was proved that the global attractors for multivalue semi-flows are the upper semi-continuity under random perturbation. This result can be used in the ntmerical approximation of multivalued semi-flows and non-autonomous perturbation of multivalued semi-flows.Key words random attractor, upper semi-continuity, absorbing set.

  14. Maximum-efficiency architectures for steady-flow combustion engines, I: Attractor trajectory optimization approach

    International Nuclear Information System (INIS)

    In this paper, we present a new systematic optimization approach to identify maximum-efficiency architectures for steady-flow combustion engines. Engine architectures are modeled as trajectories in the thermodynamic state space, and the optimal engine architecture is deduced by minimization of total irreversibility over all permissible trajectories that satisfy device constraints. In the past, both parametric and functional minimizations of engine irreversibility have been studied extensively. Our approach combines the functional optimization aspect (i.e., optimization of the process sequence or engine cycle) and the parametric optimization aspect (i.e., optimization of process lengths or parameters in the engine cycle) to identify the maximum-efficiency architecture permitted by physics. The concept central to this approach is that of chemical-equilibrium attractor states in the thermodynamic state space. It enables semi-analytical optimization for reactive engines with no need to model the detailed combustion dynamics. In this study we present the motivation and theoretical details of this method. In Part II of this study, this approach is applied to optimize the class of simple-cycle gas turbine engines. It is shown that even with modest device technology (e.g., turbine inlet temperature of 1650 K), maximum efficiency above 50% can be achieved in simple-cycle engines. - Highlights: • New irreversibility-minimization approach to identify maximum-efficiency architecture for steady-flow combustion engines. • Establishes both the optimal process sequence (engine cycle) and optimal process-length parameters. • Includes minimization of combustion irreversibility

  15. Multiple Solutions in Natural Convection in an Air Filled Square Enclosure: Fractal Dimension of Attractors

    Science.gov (United States)

    Aklouche Benouaguef, S.; Zeghmati, B.; Bouhadef, K.; Daguenet, M.

    In this study, we investigated numerically the transient natural convection in a square cavity with two horizontal adiabatic sides and vertical walls composed of two regions of same size maintained at different temperatures. The flow has been assumed to be laminar and bi-dimensional. The governing equations written in dimensionless form and expressed in terms of stream function and vorticity, have been solved using the Alternating Direction Implicit (ADI) method and the GAUSS elimination method. Calculations were performed for air (Pr = 0.71), with a Rayleigh number varying from 2.5x105 to 3.7x106. We analysed the effect of the Rayleigh number on the route to the chaos of the system. The first transition has been found from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. For sufficiently small Rayleigh numbers, present results show that the flow is characterized by four cells with horizontal and vertical symmetric axes. The attractor bifurcates from a stable fixed point to a limit cycle for a Rayleigh number varying from 2.5x105 to 2.51x105. A limit cycle settles from Ra = 3x105 and persists until Ra = 5x105. At a Rayleigh number of 2.5x105 the temporal evolution of the Nusselt number Nu(t) was stationary. As the Rayleigh number increases, the flow becomes unstable and bifurcates to a time periodic solution at a critical Rayleigh number between 2.5x105 and 2.51x105. After the first HOPF bifurcation at Ra = 2.51x105, the oscillatory flow undergoes several bifurcations and ultimately evolves into a chaotic flow.

  16. Modeling the Epigenetic Attractors Landscape: Towards a Post-Genomic Mechanistic Understanding of Development

    Directory of Open Access Journals (Sweden)

    Jose eDavila-Velderrain

    2015-04-01

    Full Text Available Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL, originally proposed by C.H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL, a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.

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

    Directory of Open Access Journals (Sweden)

    Jairo A Díaz

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

  18. Bianchi VIII and IX vacuum cosmologies: Almost every solution forms particle horizons and converges to the Mixmaster attractor

    CERN Document Server

    Brehm, Bernhard

    2016-01-01

    Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII and IX, as they approach the big bang singularity. It is known since 2001 that generic Bianchi IX spacetimes converge towards the so-called Mixmaster attractor as time goes towards the singularity. We extend this result to the case of Bianchi VIII vacuum. The BKL picture suggests that particle horizons should form, i.e. spatially separate regions should causally decouple. We prove that this decoupling indeed occurs, for Lebesgue almost every Bianchi VIII and IX vacuum spacetime.

  19. A dynamical model for hierarchy and modular organization: The trajectories en route to the attractor at the transition to chaos

    Science.gov (United States)

    Robledo, Alberto

    2012-11-01

    We show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut emergent property. This well-known nonlinear model system combines a simple and precise definition, an intricate nested hierarchical dynamical structure, and emergence of a power-law dynamical property absent in the exponential-law that governs the dynamics within the modules. This classic nonlinear system is put forward as a working example for complex collective behavior.

  20. Multiple attractors and critical parameters and how to find them numerically: the right, the wrong and the gambling way

    Science.gov (United States)

    True, Hans

    2013-03-01

    In recent years, several authors have proposed 'easier numerical methods' to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are commented upon. I also address the questions when a linearisation is allowed and the curious fact that the hunting motion is more robust than the ideal stationary-state motion on the track. Concepts such as 'multiple attractors', 'subcritical and supercritical bifurcations', 'permitted linearisation', 'the danger of running at supercritical speeds' and 'chaotic motion' are addressed.

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

    Institute of Scientific and Technical Information of China (English)

    应阳君; 黄祖洽

    2001-01-01

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

  2. CHAOS THEORY AND THE ROLE OF EXPERT ANALYSIS AS A PERIODIC ATTRACTOR DURING THE 2004 INDIAN OCEAN TSUNAMI

    Directory of Open Access Journals (Sweden)

    Matthew O’Lemmon

    2013-01-01

    Full Text Available The 2004 Indian Ocean Tsunami was epic in scale and scope and will go down as one of the largest natural disasters in human history. This paper presents an analysis of media coverage of the disaster and surveys of 206 local and international tourists in Khao Lak, Thailand, through the framework of chaos theory. Specifically, this paper examines the role of expert analysis as a periodic attractor during and after the tsunami. It will demonstrate how expert analysis brought disparate images and eyewitness testimony into greater focus, creating order in an otherwise chaotic environment.

  3. Strange attractors, spiritual interlopers and lonely wanderers:The search for pre-Pangean supercontinents

    Institute of Scientific and Technical Information of China (English)

    Joseph G. Meert

    2014-01-01

    The observation is made that there are very strong similarities between the supercontinents Columbia, Rodinia and Pangea. If plate tectonics was operating over the past 2.5 billion years of Earth history, and dominated by extroversion and introversion of ocean basins, it would be unusual for three superconti-nents to resemble one another so closely. The term‘strange attractor’ is applied to landmasses that form a coherent geometry in all three supercontinents. Baltica, Laurentia and Siberia form a group of‘strange attractors’ as do the elements of East Gondwana (India, Australia, Antarctica, Madagascar). The elements of “West Gondwana” are positioned as a slightly looser amalgam of cratonic blocks in all three super-continents and are referred to as ‘spiritual interlopers’. Relatively few landmasses (the South China, North China, Kalahari and perhaps Tarim cratons) are positioned in distinct locations within each of the three supercontinents and these are referred to as‘lonely wanderers’. There may be several explanations for why these supercontinents show such remarkable similarities. One possibility is that modern-style plate tectonics did not begin until the late Neoproterozoic and horizontal motions were restricted and a vertical style of ‘lid tectonics’ dominated. If motions were limited for most of the Proterozoic, it would explain the remarkable similarities seen in the Columbia and Rodinia supercontinents, but would still require the strange attractors to rift, drift and return to approximately the same geometry within Pangea. A second possibility is that our views of older supercontinents are shaped by well-known connections documented for the most recent supercontinent, Pangea. It is intriguing that three of the four ‘lonely wanderers’ (Tarim, North China, South China) did not unite until just before, or slightly after the breakup of Pangea. The fourth‘lonely wanderer’, the Kalahari (and core Kaapvaal) craton has a somewhat

  4. In-in and δN calculations of the bispectrum from non-attractor single-field inflation

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Xingang [Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Cambridge, CB3 0WA (United Kingdom); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Komatsu, Eiichiro [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, Garching, 85741 (Germany); Namjoo, Mohammad Hossein [School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Sasaki, Misao, E-mail: xingang.chen@utdallas.edu, E-mail: firouz@ipm.ir, E-mail: komatsu@mpa-garching.mpg.de, E-mail: mh.namjoo@ipm.ir, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for theoretical Physics, Kyoto University, Kyoto, 606–8502 (Japan)

    2013-12-01

    In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as R∝a{sup 3}. This is so far the only known class of self-consistent single-field models with a Bunch-Davies initial state that can produce a large squeezed-limit bispectrum violating Maldacena's consistency relation. Given the importance of this result, we calculate the bispectrum with three different methods: using quantum field theory calculations in two different gauges, and classical calculations (the δN formalism). All the results agree, giving the local-form bispectrum parameter of f{sup local}{sub NL} = 5(1+c{sub s}{sup 2})/(4c{sub s}{sup 2}). This result is valid for arbitrary values of the speed of sound parameter, c{sub s}, for a particular non-attractor model we consider in this paper.

  5. Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators

    Science.gov (United States)

    Kengne, J.; Njitacke Tabekoueng, Z.; Fotsin, H. B.

    2016-07-01

    We perform a systematic analysis of a system consisting of an autonomous third order Duffing-Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.

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

    Institute of Scientific and Technical Information of China (English)

    陆宏伟; 陈亚珠; 卫青

    2004-01-01

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

  7. HYPERSOCIETY AS THE ATTRACTOR OF THE SOCIAL SYSTEM EVOLUTION (PART 2: THE FEATURES OF THE NEW CIVILIZATION

    Directory of Open Access Journals (Sweden)

    Филипп Иванович Розанов

    2013-09-01

    Full Text Available This article is the attempt to apply the system approach for the long-term prognosis of civilization development and substantiation of the concept of the Hypersociety as the attractor of the evolution of social systems. Determined by the principles of the system prognosis. Analyzes the factors of metasystem transition to the Hypersociety and distinguish the main features of the new level of social organization. Considered questions of biological, psychological and technological development of human and society. Revealed specific structural and functional organization of Hypersociety and its relationship with Nature. This article introduces several new scientific concepts: Hypersociety, Socione, Technoevolution, Hypernetwork, Metaculture. The results of this research have principal importance for determining the prospects of civilizational development, in consequence of which are necessary for social science theorists and managers, as well as may be interesting for technical specialists.DOI: http://dx.doi.org/10.12731/2218-7405-2013-6-32

  8. Crosstalk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: Phase diagram

    Science.gov (United States)

    Monasson, R.; Rosay, S.

    2013-06-01

    We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding one-dimensional (1D) or 2D spatial maps or environments. Different maps correspond to random allocations (permutations) of the place fields. Based on replica calculations we show that, below critical levels for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the crosstalk between the maps, and memory of environments is lost. Remarkably the spatially localized regime is very robust against the neural noise until it reaches its critical level. Numerical simulations are in excellent quantitative agreement with our theoretical predictions.

  9. Uniqueness of Attractors for Semigroups of Class(H)%(H)类半群的吸引子的唯一性

    Institute of Scientific and Technical Information of China (English)

    葛根哈斯

    2000-01-01

    It is proved that the minimal closed global B-attractor coincides with the minimal closed global B-attractor (M) for the B-dissipative (or bounded and pointwise dissipative) continuous semigroup of class(H)if the semigroup is pointwise invertible on M and positively Poisson-stable points are dense in M.%对于B-耗散(或有界且逐点耗散)的连续(H)类半群的极小全局B-吸引子M及极小全局吸引子(M)证明了:如果半群在M上是逐点可逆的且M的稠子集上的运动是Poisson稳定的,则有M≡(M).

  10. IN-MACA-MCC: Integrated Multiple Attractor Cellular Automata with Modified Clonal Classifier for Human Protein Coding and Promoter Prediction

    Directory of Open Access Journals (Sweden)

    Kiran Sree Pokkuluri

    2014-01-01

    Full Text Available Protein coding and promoter region predictions are very important challenges of bioinformatics (Attwood and Teresa, 2000. The identification of these regions plays a crucial role in understanding the genes. Many novel computational and mathematical methods are introduced as well as existing methods that are getting refined for predicting both of the regions separately; still there is a scope for improvement. We propose a classifier that is built with MACA (multiple attractor cellular automata and MCC (modified clonal classifier to predict both regions with a single classifier. The proposed classifier is trained and tested with Fickett and Tung (1992 datasets for protein coding region prediction for DNA sequences of lengths 54, 108, and 162. This classifier is trained and tested with MMCRI datasets for protein coding region prediction for DNA sequences of lengths 252 and 354. The proposed classifier is trained and tested with promoter sequences from DBTSS (Yamashita et al., 2006 dataset and nonpromoters from EID (Saxonov et al., 2000 and UTRdb (Pesole et al., 2002 datasets. The proposed model can predict both regions with an average accuracy of 90.5% for promoter and 89.6% for protein coding region predictions. The specificity and sensitivity values of promoter and protein coding region predictions are 0.89 and 0.92, respectively.

  11. IN-MACA-MCC: Integrated Multiple Attractor Cellular Automata with Modified Clonal Classifier for Human Protein Coding and Promoter Prediction

    Science.gov (United States)

    Pokkuluri, Kiran Sree; Inampudi, Ramesh Babu; Nedunuri, S. S. S. N. Usha Devi

    2014-01-01

    Protein coding and promoter region predictions are very important challenges of bioinformatics (Attwood and Teresa, 2000). The identification of these regions plays a crucial role in understanding the genes. Many novel computational and mathematical methods are introduced as well as existing methods that are getting refined for predicting both of the regions separately; still there is a scope for improvement. We propose a classifier that is built with MACA (multiple attractor cellular automata) and MCC (modified clonal classifier) to predict both regions with a single classifier. The proposed classifier is trained and tested with Fickett and Tung (1992) datasets for protein coding region prediction for DNA sequences of lengths 54, 108, and 162. This classifier is trained and tested with MMCRI datasets for protein coding region prediction for DNA sequences of lengths 252 and 354. The proposed classifier is trained and tested with promoter sequences from DBTSS (Yamashita et al., 2006) dataset and nonpromoters from EID (Saxonov et al., 2000) and UTRdb (Pesole et al., 2002) datasets. The proposed model can predict both regions with an average accuracy of 90.5% for promoter and 89.6% for protein coding region predictions. The specificity and sensitivity values of promoter and protein coding region predictions are 0.89 and 0.92, respectively. PMID:25132849

  12. Oscillatory neurocomputing with ring attractors: a network architecture for mapping locations in space onto patterns of neural synchrony.

    Science.gov (United States)

    Blair, Hugh T; Wu, Allan; Cong, Jason

    2014-02-01

    Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned 'grid cells' can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting 'theta cells' that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony. PMID:24366137

  13. Oscillatory neurocomputing with ring attractors: a network architecture for mapping locations in space onto patterns of neural synchrony.

    Science.gov (United States)

    Blair, Hugh T; Wu, Allan; Cong, Jason

    2014-02-01

    Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned 'grid cells' can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting 'theta cells' that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony.

  14. The 3-Attractor Water Model: Monte-Carlo Simulations with a New, Effective 2-Body Potential (BMW

    Directory of Open Access Journals (Sweden)

    Francis Muguet

    2003-02-01

    Full Text Available According to the precepts of the 3-attractor (3-A water model, effective 2-body water potentials should feature as local minima the bifurcated and inverted water dimers in addition to the well-known linear water dimer global minimum. In order to test the 3-A model, a new pair wise effective intermolecular rigid water potential has been designed. The new potential is part of new class of potentials called BMW (Bushuev-Muguet-Water which is built by modifying existing empirical potentials. This version (BMW v. 0.1 has been designed by modifying the SPC/E empirical water potential. It is a preliminary version well suited for exploratory Monte-Carlo simulations. The shape of the potential energy surface (PES around each local minima has been approximated with the help of Gaussian functions. Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble for a very wide range of state parameters up to the supercritical water regime. Thermodynamic properties are reported. The radial distributions functions (RDFs have been computed and are compared with the RDFs obtained from Neutron Scattering experimental data. Our preliminary Monte-Carlo simulations show that the seemingly unconventional hypotheses of the 3-A model are most plausible. The simulation has also uncovered a totally new role for 2-fold H-bonds.

  15. Attractors of hybrid magnetic levitation ball system and stability research%混合磁悬浮球系统吸引子及稳定性研究

    Institute of Scientific and Technical Information of China (English)

    马凤莲; 江东; 张翔; 杨嘉祥

    2012-01-01

    为了避免磁悬浮球混沌运动,设计了永磁和电磁混合型磁悬浮球模型,推导了磁悬浮球的动力学方程,并建立了磁悬浮球系统的仿真模型.通过改变初始状态,得到不同初始条件下的磁悬浮球系统吸引子.混合型磁悬浮球系统具有单、双两类吸引子,双吸引子表现出较强的混沌特性,磁悬浮球围绕平衡点附近的波动较大,磁悬浮球由混沌运动状态向非混沌运动状态转变时,由双吸引子逐渐向单吸引子过渡,系统演变为具有周期特性的运动状态,再演变为相轨迹收敛于一个点,磁悬浮球处于较稳定的运动状态.仿真和实验结果表明,通过磁悬浮球吸引子的研究可了解混沌产生的初始区间,进而为设计中避开混沌区实现磁悬浮球的稳定运动提供了参考依据.%In order to avoid magnetic levitation ball in the chaotic region, the model of permanent magnet and electromagnet hybrid magnetic levitation ball system was designed,the dynamic equation of magnetic levitation ball was deduced, and the magnetic levitation system simulation mode] was set up. The different attractors were obtained by changing the initial states. The simulation results show that the hybrid magnetic levitation ball system designed has single and double two types of attractors. The double attractors have stronger chaotic performance and the magnetic levitation ball has greater fluctuation around the equilibrium point. The attractor is gradually from double attractors to single attractor in magnetic levitation ball from chaotic station transition to non-chaotic state, the magnetic levitation ball becomes a cyclical nature of the motion state and it gradually evolves to a point of phase trajectories when the system presents a stable state. Simulation and test show that the chaos generated by the initial region can be understood by studying the magnetic levitation ball attractors, which provides a reference design basis to a

  16. The oldest computer in today's education: The great attractor of children to science, the Antikythera Mechanism, as an educational instrument.

    Science.gov (United States)

    Moussas, X.; Coustenis, A.; Solomonidou, A.; Bampasidis, G.; Bratsolis, E.; Stamogiorgos, S.

    2012-04-01

    People have always been charmed by the beauty of the starry sky, the Sun, the Moon, the planets, the Solar System and the mystery of the birth and the evolution of the Cosmos. As the deep space is believed to be the only territory unexplored by the mankind, the humanity has always been looking forward to the discoveries of Space Science. However, due to the complicated character of modern Science and Technology, people usually are alienated from scientific issues. Dealing with this situation, the Space Group of the National and Kapodistrian University of Athens in collaboration with LESIA of the Observatoire de Paris-Meudon, have been performing several campaigns to raise the public awareness of Science and Astronomy with emphasis to the Solar System exploration. The Space Group of the University of Athens has scientific impact in both the Space Physics field and the public outreach of Astronomy throughout Europe, Northern Africa and the United States of America. Using the Antikythera Mechanism as central object and as a great attractor of children and the general public to astronomy and even philosophy, we have performed numerous outreach activities focalized on the general audience in order to conceptualize astronomical phenomena and change their prior usually not very clear knowledge and intuition. These Solar System events, conducted by our Group, help young people to develop their critical thinking, self-expression and creative talents and eventually to love astronomy and to develop an interest the planets. Their introduction into the space field seems essential for cultivation of these skills.

  17. Noise Stabilized Random Attractor

    OpenAIRE

    Finn, J.M.; Tracy, E. R.; Cooke, W. E.; Richardson, A. S.

    2005-01-01

    A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts on either side of x = 0, separated by the presence of an invariant manifold at x = 0. In the presence of arbitrarily small additive noise in the x direction, the successive bursts have bounded amplitudes and interburst intervals. This system with noise is ...

  18. Quantum Attractor Flows

    CERN Document Server

    Gunaydin, Murat; Pioline, Boris; Waldron, Andrew

    2007-01-01

    Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M^*_3, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions t...

  19. Dimension estimate for global attractor of a class of nonlinear beam equation%一类非线性梁方程全局吸引子的维数估计

    Institute of Scientific and Technical Information of China (English)

    姜金平; 张晓明; 董超雨

    2015-01-01

    The nonlinear beam equations represent the viberation of the rode bed in downward direction .Based on the existence of global attractors in other article ,this paper proved that semigroup S(t) generated by a class of nonlinear beam equation was uniformly differentiable on the global attractor Α.The paper also proved that global attractors of this class of equation have limited fractal dimension .Furthermore ,an estimate was given with the application of Sobolev‐Lieb‐Thirring inequality and upper bound of fractal dimension of the global attractor is obtained .%非线性梁方程描述了桥面竖直平面内的振动。在以往文献的基础上证明了一类非线性梁方程生成的解半群 S(t)在全局吸引子Α上是一致可微,其全局吸引子具有有限的分形维数,并进一步应用Sobolev‐Lieb‐T hirring不等式进行估计,得到全局吸引子的分形维数的上界。

  20. Approximations of chaotic attractors and its circuit design based on the parameter switching algorithm%基于参数切换算法的混沌系统吸引子近似及其电路设计∗

    Institute of Scientific and Technical Information of China (English)

    罗少轩; 何博侠; 乔爱民; 王艳春

    2015-01-01

    Based on the parameter switching algorithm and the discrete chaotic system, a new chaotic system based parameter switching algorithm is proposed. The principles of parameter switching algorithm and chaotic system based parameter switching algorithm are presented in detail by means of flow chart and step description. By applying phase diagram observation method, chaotic attractor approximation of the unified chaotic system is investigated based on parameter switching algorithm and chaotic system based parameter switching algorithm. It shows that chaos can be obtained by switching two periodic parameters and periodic state can be observed by switching two chaotic parameters. Thus the formulas chaos + chaos = periodic and period + period = chaos are proved to be workable in this paper. Chaotic attractor approximation of Rössler chaotic system is also studied by employing the two switching methods. Two cases are investigated. Firstly, a chaotic switching system is obtained by switching a chaotic parameter and a periodic parameter. Then a more complex switching scheme is carried out. Periodic system is switched by two periodic parameters and a chaotic parameter. So, the formulas chaos+periodic=chaos and periodic+period+chaos=periodic are proved to be workable. It shows that the switching system is the approximation of the original system under specified parameter, and the attractor is in accordance with the attractor of the targeting system. The outputs of the Logistic map based parameter switching algorithm are more complex than those of existing parameter switching algorithm. As the distribution of logistic map is not uniform, the approximate attractor does not consist of the targeting system and shows more complicated structure. But approximate attractors can be obtained when the distribution of discrete sequence is uniform. In addition, the chaotic map based parameter switching algorithm has larger secret key space since it has the initial values and parameter of

  1. Existence of Global Attractors in for -Laplacian Parabolic Equation in

    OpenAIRE

    Chen Caisheng; Shi Lanfang; Wang Hui

    2009-01-01

    Abstract We study the long-time behavior of solution for the -Laplacian equation in , in which the nonlinear term is a function like with , , or with and . We prove the existence of a global -attractor for any .

  2. Exponential Attractor for the Derivative Two dimensional Ginaburg-Landau Equation in Banach Spaces%二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

    Institute of Scientific and Technical Information of China (English)

    黄健; 戴正德

    2004-01-01

    在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.

  3. Parkes HI observations of galaxies behind the southern Milky Way. II. The Crux and Great Attractor regions (l ~ 289 degree to 338 degree)

    CERN Document Server

    Schroeder, Anja C; Henning, Patricia A

    2009-01-01

    As part of our programme to map the large-scale distribution of galaxies behind the southern Milky Way, we observed 314 optically-selected, partially-obscured galaxies in the Zone of Avoidance (ZOA) in the Crux and Great Attractor (GA) regions. The observations were conducted with the Parkes 64m radio telescope, in a single-pixel pointed mode, reaching an rms noise level of typically 2-6 mJy over the velocity search range of 400

  4. Multiple Attractor Cellular Automata Classification Method and Over-Fitting Problem with CART%分类回归树多吸引子细胞自动机分类方法及过拟合研究

    Institute of Scientific and Technical Information of China (English)

    方敏; 牛文科; 张晓松

    2012-01-01

    基于多吸引子细胞自动机的分类方法多是二分类算法,难以克服过度拟合问题,在生成多吸引子细胞自动机时如何有效地处理多分类及过度拟合问题还缺乏可行的方法.从细胞空间角度对模式空间进行分割是一种均匀分割,难以适应空间非均匀分割的需要.将CART算法同多吸引子细胞自动机相结合构造树型结构的分类器,以解决空间的非均匀分割及过度拟合问题,并基于粒子群优化方法提出树节点的最优多吸引子细胞自动机特征矩阵的构造方法.基于该方法构造的多吸引子细胞自动机分类器能够以较少的伪穷举域比特数获得好的分类性能,减少了分类器中的空盆数量,在保证分类正确率的同时改善了过拟合问题,缩短了分类时间.实验分析证明了所提出方法的可行性和有效性.%The classification methods based on multiple attractor cellular automata can process the classification of two classes, and they are difficult to overcome overfitting problem. There are not yet effective methods for constructing a multiple attractor cellular automata which can process multi-classification and overfitting problem. The pattern space partition in the view of cell space is a kind of uniform partition which is difficult to adapt to the needs of spatial non-uniform partition. By combining the CART algorithm with the multiple attractor cellular automata, a kind of classifier with tree structure is constructed to solve the non-uniform partition problem and overfitting problem. The multiple attractor cellular automata characteristic matrix is defined, and the learning method of classifiers as a node in a tree is studied based on particle swarm optimization algorithm. The multiple attractor cellular automata classifiers built on this approach are able to obtain good classification performance by using less number of bits of pseudo-exhaustive field. The classifier with tree frame of multiple

  5. Global Attractor of Strong Solution for the Penalized 2D Navier-Stokes Equation%带惩罚项的二维Navier-Stokes方程的强解的全局吸引子

    Institute of Scientific and Technical Information of China (English)

    薛自学

    2011-01-01

    Based on the abstract results given in paper[8] ,the existence of global attractor of strong solution for penalized 2D Navier-Stokes equations has been proved by using the semigroup approach.%根据文献[8]中给出的全局吸引子的抽象结果,利用半群的方法证明了带惩罚项的二维Navier-Stokes方程的强解的全局吸引子的存在性.

  6. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    International Nuclear Information System (INIS)

    Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

  7. Preseismic oscillating electric field "strange attractor like" precursor, of T = 6 months, triggered by Ssa tidal wave. Application on large (Ms > 6.0R) EQs in Greece (October 1st, 2006 - December 2nd, 2008)

    CERN Document Server

    Thanassoulas, C; Verveniotis, G; Zymaris, N

    2009-01-01

    In this work the preseismic "strange attractor like" precursor is studied, in the domain of the Earth's oscillating electric field for T = 6 months. It is assumed that the specific oscillating electric field is generated by the corresponding lithospheric oscillation, triggered by the Ssa tidal wave of the same wave length (6 months) under excess strain load conditions met in the focal area of a future large earthquake. The analysis of the recorded Earth's oscillating electric field by the two distant monitoring sites of PYR and HIO and for a period of time of 26 months (October 1st, 2006 - December 2nd, 2008) suggests that the specific precursor can successfully resolve the predictive time window in terms of months and for a "swarm" of large EQs (Ms > 6.0R), in contrast to the resolution obtained by the use of electric fields of shorter (T = 1, 14 days, single EQ identification) wave length. More over, the fractal character of the "strange attractor like" precursor in the frequency domain is pointed out. Fina...

  8. Invariability, orbits and fuzzy attractors

    Science.gov (United States)

    Perez-Gonzaga, S.; Lloret-Climent, M.; Nescolarde-Selva, J. A.

    2016-01-01

    In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality.

  9. Free Energy, Value, and Attractors

    Directory of Open Access Journals (Sweden)

    Karl Friston

    2012-01-01

    Full Text Available It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable states they expect to encounter.

  10. Unity of Cosmological Inflation Attractors

    NARCIS (Netherlands)

    Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik

    2015-01-01

    Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These

  11. The Unity of Cosmological Attractors

    NARCIS (Netherlands)

    Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik

    2015-01-01

    Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $\\xi$-att

  12. Photonic analogies of gravitational attractors

    KAUST Repository

    San-Román-Alerigi, Damián P.

    2013-01-01

    In our work we demonstrate a Gaussian-like refractive index mapping to realize light trapping. Our study shows that this centro-symmetrical photonic structure is able to mime the light geodesics described by celestial mechanics. Possible applications are discussed. © 2013 IEEE.

  13. Some properties for the attractors

    Institute of Scientific and Technical Information of China (English)

    ZHENG; Zuohuan

    2001-01-01

    [1]Conley,C.,Isolated invariant sets and the morse index,CBMS Regional Conf.Ser.in Math.,No.38,Providence,RI:Amer.Math.Soc.,1978.[2]Conley,C.,The gradient structure of a flow:1,Ergod.Th.& Dynam.Sys.,1988,8 (1):11-26.[3]Yu Shuxiang,The existence of trajectories joining critical points,J.Differential Equations,1987,66(2):230-242.[4]Conley,C.,Easton,R.,Isolated invariant sets and isolating blocks,Trans.Amer.Math.Soc.,1971,158(1):35-61.[5]Frank,J.,Selgrade,J.,Abstract ω-limit sets,chain recurrent sets,and basic sets for flows,Proc.Amer.Math.Soc.,1976,60(3):309-316.[6]Nitecki,Z.,Explosions in completely unstable flows 1,Trans.Amer.Math.Soc.,1978,245(1):43-61.[7]Conley,C.,Zehnder,E.,The Birkhoff-Lewis fixed point theorem and a conjecture of V.I.Arnold,Invent.Math.,1983,73(1):33-49.[8]Smale,S.,Morse inequilities for a dynamical system.Bull.Amer.Math.Soc.,1960,66(1):43-49.[9]Selgrade,J.,Isolated invariant sets for flows on vector bundles,Trans.Amer.Math.Soc.,1975,203(3):359-390.[10]Franks,J.,Constructing stable diffeomorphisms,Ann.of Math.,1977,105(3):343-359.[11]Eisenberg,M.,Topology,New York:Holt,Rinehart and Winston,Inc.,1974.[12]Nemytskii,V.V.,Stepanov,V.V.,Qualitative Theory of Differential Equations,Princeton:Princeton Univ.Press,1960.[13]Huang Tusen,The note on limit set of a set and the non-wandering set,J.Ningbo University,1997,10(2):1-8.[14]Huang Tusen,Compact and asymptotic stability of the set of bounded solutions,J.Hainan Teachers College,1997,8:9-15.

  14. Generation of Chaotic Attractor Parameter Vectors with Frieze Groups Based on PSO%基于粒子群算法的带群混沌吸引子参数的生成

    Institute of Scientific and Technical Information of China (English)

    赵娜; 王化雨

    2012-01-01

    Taking the model of pl al-equivarieot mappings of frieze groups for example .discuss in detail the model's structure methods and processes. Introduce a proposal to extend the heuristic called " particle swarm optimization" (PSO) to deal with the problem of searching chaotic parameters of chaotic attractors with planar frieze symmetries in the multi-parameter space, and propose a novel particle presentation for the chaotic parameter vectors. Experimental results indicate that the PSO can effectively and quickly get optimal resolution of the chaotic parameter vectors and avoid the " genetic drift" phenomenon from the eugenic genetic algorithm effectively,so it is proved to be an effective method for the optimization of parameter vector, solving the problem of generating chaotic attractors with planar frieze symmetries in large parameter space difficultly.%文中以带群等价映射模型p1a1为例,详细论述了模型p1a1混沌吸引子的构造方法与过程.将粒子群算法(PSO)应用于搜索具有平面带群对称性混沌吸引子的参数问题,构造了参数向量作为粒子的表达方法,建立了此问题的粒子群算法.试验结果表明,粒子群算法可以快速、有效求得各参数向量的最优解,并且有效地避免了优生遗传算法的“遗传漂移”问题,是优化参数向量的一个较好方案,从而解决了在巨大参数空间下生成具有平面带群对称性混沌吸引子困难的问题.

  15. Preseismic electric field "strange attractor" like precursor analysis applied on large (Ms > 5.5R) EQs, which occurred in Greece during December 1st, 2007 - April 30th, 2008

    CERN Document Server

    Thanassoulas, C; Verveniotis, G; Zymaris, N

    2008-01-01

    In order to investigate the capability of the preseismic electric field "strange attractor like" precursor as a time predictor of a large EQ within a short time window (short-term prediction), the specific methodology was applied on the Earth's electric field recorded during a rather long seismically active period (December 1st, 2007 - April 30th, 2008) of Greece. During this period of time a number (8) of large (Ms > 5.5R) earthquakes took place. The particular analysis is presented in detail for the following EQs: the Monemvasia EQ (January 6th 2008, Ms = 6.6R), the Methoni EQs (February 14th 2008 Ms = 6.7R, February 19th 2008 Ms = 5.6R, February 20th 2008 Ms = 6.5R, February 26th 2008 Ms = 5.7R), the Skyros EQ (March 19th 2008 Ms = 5.5R) and the Mid Southern Creta EQ (March 28th 2008 Ms = 5.6R). The obtained results from the analysis of the afore mentioned EQs, in conjunction to the ones obtained from an earlier presentation of the particular methodology (Thanassoulas et al. 2008a), suggest: an average tim...

  16. Attractors, bifurcations, & chaos nonlinear phenomena in economics

    CERN Document Server

    Puu, Tönu

    2003-01-01

    The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ­ ent, as it also included some chapters with mathematical background mate­ rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus­ trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math­ ematics ch...

  17. Noise-assisted estimation of attractor invariants.

    Science.gov (United States)

    Restrepo, Juan F; Schlotthauer, Gastón

    2016-07-01

    In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K_{2}), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (D_{m}^{U}), the correlation entropy (K_{m}^{U}), and the noise level (σ_{m}^{U}). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators D_{m}^{U} and σ_{m}^{U} behave in a similar manner to those based on the GCI. However, for the calculation of K_{2}, the estimator K_{m}^{U} outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K_{2}, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants. PMID:27575128

  18. Noise-assisted estimation of attractor invariants

    Science.gov (United States)

    Restrepo, Juan F.; Schlotthauer, Gastón

    2016-07-01

    In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D ), the correlation entropy (K2), and the noise level (σ ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U -correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D ,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.

  19. The SD oscillator and its attractors

    International Nuclear Information System (INIS)

    We propose a new archetypal oscillator for smooth and discontinuous systems (SD oscillator). This oscillator behaves both smooth and discontinuous system depending on the value of the smoothness parameter. New dynamic behaviour is presented for the transitions from the smooth to discontinuous regime

  20. The SD oscillator and its attractors

    Energy Technology Data Exchange (ETDEWEB)

    Cao, Q [Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043 (China); Wiercigroch, M; Pavlovskaia, E; Grebogi, C; Michael, J; Thompson, T [Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, King' s College, Aberdeen AB24 3UE, Scotland (United Kingdom)], E-mail: qingjiecao@hotmail.com

    2008-02-15

    We propose a new archetypal oscillator for smooth and discontinuous systems (SD oscillator). This oscillator behaves both smooth and discontinuous system depending on the value of the smoothness parameter. New dynamic behaviour is presented for the transitions from the smooth to discontinuous regime.

  1. The SD oscillator and its attractors

    Science.gov (United States)

    Cao, Q.; Wiercigroch, M.; Pavlovskaia, E.; Grebogi, C.; Michael, J.; Thompson, T.

    2008-02-01

    We propose a new archetypal oscillator for smooth and discontinuous systems (SD oscillator). This oscillator behaves both smooth and discontinuous system depending on the value of the smoothness parameter. New dynamic behaviour is presented for the transitions from the smooth to discontinuous regime.

  2. The attractor mechanism as a distillation procedure

    CERN Document Server

    Lévay, Péter

    2010-01-01

    In a recent paper it has been shown that for double extremal static spherically symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of GHZ-type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a GHZ state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macros...

  3. Noise-assisted estimation of attractor invariants.

    Science.gov (United States)

    Restrepo, Juan F; Schlotthauer, Gastón

    2016-07-01

    In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K_{2}), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (D_{m}^{U}), the correlation entropy (K_{m}^{U}), and the noise level (σ_{m}^{U}). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators D_{m}^{U} and σ_{m}^{U} behave in a similar manner to those based on the GCI. However, for the calculation of K_{2}, the estimator K_{m}^{U} outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K_{2}, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.

  4. Moduli stabilization, large-volume dS minimum without D3{sup -bar} -branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's

    Energy Technology Data Exchange (ETDEWEB)

    Misra, Aalok [Department of Physics, Indian Institute of Technology, Roorkee 247 667, Uttaranchal (India); Physics Department, Theory Unit, CERN, CH-1211 Geneva 23 (Switzerland)], E-mail: aalokfph@iitr.ernet.in; Shukla, Pramod [Department of Physics, Indian Institute of Technology, Roorkee 247 667, Uttaranchal (India)], E-mail: pmathdph@iitr.ernet.in

    2008-08-11

    We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of 'area codes' [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, (hep-th/0511215)] and the possibility of getting a non-supersymmetric dS minimum without the addition of D3-bar-branes as in KKLT for type II flux compactifications. The second has to do with the 'inverse problem' [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, (hep-th/0703214)] and 'fake superpotentials' [A. Ceresole, G. Dall'Agata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, (hep-th/0702088)] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a 'Swiss cheese' Calabi-Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, (hep-th/0505076)] expressed as a degree-18 hypersurface in WCP{sup 4}[1,1,1,6,9] in the 'large-volume-scenario' limit [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 0503 (2005) 007, (hep-th/0502058)]. The main result of our paper is that we show that by including non-perturbative {alpha}{sup '} and instanton corrections in the Kaehler potential and superpotential [T.W. Grimm, Non-perturbative corrections and modularity in N=1 type IIB compactifications, (arXiv: 0705.3253 [hep-th])], it may be possible to obtain a large-volume non-supersymmetric dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi-Yau has been of relevance also from the point of other studies of Kaehler moduli stabilization via non-perturbative instanton contributions [F. Denef, M.R. Douglas, B. Florea, Building a better racetrack, JHEP 0406 (2004) 034, (hep-th/0404257)] and non-supersymmetric AdS vacua (and their

  5. 萤火虫邻域结构的多吸引子微粒群算法及应用——以中国台湾再制造资源回收处理中心选址规划为例%Multi-attractors PSO with glowworm neighborhood space and is application——location planning for the remanufacturing resource recycling centers in Taiwan China.

    Institute of Scientific and Technical Information of China (English)

    叶林; 叶春明; 胡金涛

    2011-01-01

    This paper puts forward a multi-attractors PSO that borrows the ideas of dynamic neighborhood space from the glowworm swarm optimization. Thus it can search the solution space parallelly with multi-subgroup to improve the speed of solving. It also avoids the problem of falling into the local extremum, which is attracted by a single attractor. The multi-attractors PSO with the glowworm neighborhood space is applied to the location planning for the remanufacturing resource recycling centers in Taiwan China. The results show that the algorithm can solve this problem and assign the recycle depots successfully,with the objective of minimizing the total transportation distance.%借鉴萤火虫最优化算法的动态邻域空间结构,提出一种改进的多吸引子微粒群算法,从而能够对解空间减进行多子群并行搜索,提高求解速度,避免陷入单点局部极值.并将该算法应用到中国台湾再制造资源回收处理中心的选址规划问题中,在运输总距离最短的目标下,成功地解决了再制造资源回收处理中心的选址规划问题并对资源回收站进行了有效的指派分配.

  6. Einstein spaces as attractors for the Einstein flow

    OpenAIRE

    Andersson, L.; Moncrief, V.

    2009-01-01

    In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n + 1$-dimensional, spatially compact spacetimes, which generalizes the $k = -1$ Friedmann-Lemaître-Robertson-Walker vacuum spacetime. This work extends the result from Future complete vacuum spacetimes. The background spacetimes we consider are Lorentz cones over negative Einstein spaces of dimension $n \\ge 3$. ¶ We use a varian...

  7. Recurrence analysis and synchronization of oscillators with coexisting attractors

    Energy Technology Data Exchange (ETDEWEB)

    Kwuimy, C.A. Kitio, E-mail: kwuimy@yahoo.fr [Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085 (United States); Kadji, H.G. Enjieu, E-mail: hkadji@monell.org [Monell Chemical Senses Center, 3500 Market Street, Philadelphia, PA 19104 (United States)

    2014-06-13

    Highlights: • We establish existence conditions for limit cycles in an enzyme–substrate reaction. • The recurrence quantification analysis is utilized to explore the system behavior. • Birhythmicity, various bifurcations and chaos are analyzed. • The cross recurrence analysis is utilized to investigate synchronization states. • Chaos synchronization mostly occurs for negative values of the coupling strength. - Abstract: The method of recurrence plots (RPs) has been traditionally used for experimental time series analysis with no comparison with the mathematical model. This is in part because of lack of nonlinear analysis of mathematical model based on the recurrence quantification analysis (RQA) parameters. The paper provides substantial information about the mathematical and numerical analysis and synchronization of a multi-limit cycle oscillator from the RQA perspective. The recurrence quantification analysis parameters are used to discuss the birhythmic behavior of the system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response. Finally, the results of the method of RPs are compared to those of phase diagrams and the problem of synchronization of limit cycle and chaotic response is discussed by the mean of cross recurrence.

  8. On the number of attractors of Boolean automata circuits

    OpenAIRE

    Demongeot, Jacques; Noual, Mathilde; Sené, Sylvain

    2009-01-01

    In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on th...

  9. Random Boolean Networks and Attractors of their Intersecting Circuits

    OpenAIRE

    Demongeot, Jacques; Elena, Adrien; Noual, Mathilde; Sené, Sylvain

    2011-01-01

    International audience The multi-scale strategy in studying biological regulatory networks analysis is based on two level of analysis. The first level is structural and consists in examining the architecture of the interaction graph underlying the network and the second level is functional and analyse the regulatory properties of the network. We apply this dual approach to the "immunetworks" involved in the control of the immune system. As a result, we show that the small number of attract...

  10. Navigating cancer network attractors for tumor-specific therapy

    DEFF Research Database (Denmark)

    Creixell, Pau; Schoof, Erwin; Erler, Janine Terra;

    2012-01-01

    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...... 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....

  11. Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism

    OpenAIRE

    Kar, Supriya; Majumdar, Sumit

    2006-01-01

    We revisit the 4D generalized black hole geometries, obtained by us [1], 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 $AdS_5$ obtained in effective string theory is shown...

  12. A possible approach on optical analogues of gravitational attractors

    CERN Document Server

    San-Román-Alerigi, Damián P; Ng, Tien K; Alsunaidi, Mohammad; Ooi, Boon S; 10.1364/OE.21.008298

    2013-01-01

    In this paper we report on the feasibility of light confinement in orbital geodesics on stationary, planar, and centro-symmetric refractive index mappings. Constrained to fabrication and [meta]material limitations, the refractive index, n, has been bounded to the range: $0.8\\leq n(\\vec r)\\leq 3.5$. Mappings are obtained through the inverse problem to the light geodesics equations, considering trappings by generalized orbit conditions defined \\emph{a priori}. Our simulation results show that the above mentioned refractive index distributions trap light in an open orbit manifold, both perennial and temporal, in regards to initial conditions. Moreover, due to their characteristics, these mappings could be advantageous to optical computing and telecommunications, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments in the...

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

    International Nuclear Information System (INIS)

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

  14. Bistable Chimera Attractors on a Triangular Network of Oscillator Populations

    DEFF Research Database (Denmark)

    Martens, Erik Andreas

    2010-01-01

    We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population....... This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are...

  15. A possible approach on optical analogues of gravitational attractors

    KAUST Repository

    San-Román-Alerigi, Damián P.

    2013-04-01

    In this paper we report on the feasibility of light confinement in orbital geodesics on stationary, planar, and centro-symmetric refractive index mappings. Constrained to fabrication and [meta]material limitations, the refractive index, n, has been bounded to the range: 0.8 ? n(r) ? 3.5. Mappings are obtained through the inverse problem to the light geodesics equations, considering trappings by generalized orbit conditions defined a priori. Our simulation results show that the above mentioned refractive index distributions trap light in an open orbit manifold, both perennial and temporal, in regards to initial conditions. Moreover, due to their characteristics, these mappings could be advantageous to optical computing and telecommunications, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments in the laboratory. © 2013 Optical Society of America.

  16. A C-Function For Non-Supersymmetric Attractors

    CERN Document Server

    Goldstein, K; Mandal, G; Trivedi, S P; Goldstein, Kevin; Jena, Rudra P.; Mandal, Gautam; Trivedi, Sandip P.

    2006-01-01

    We present a c-function for spherically symmetric, static and asymptotically flat solutions in theories of four-dimensional gravity coupled to gauge fields and moduli. The c-function is valid for both extremal and non-extremal black holes. It monotonically decreases from infinity and in the static region acquires its minimum value at the horizon, where it equals the entropy of the black hole. Higher dimensional cases, involving $p$-form gauge fields, and other generalisations are also discussed.

  17. The Lukash Plane-Wave Attractor and Relative Energy

    CERN Document Server

    Korunur, M; Salti, M; Aydogdu, Oktay; Korunur, Murat; Salti, Mustafa

    2006-01-01

    We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VII$_{\\delta}$ spacetimes described by the Lukash metric. In order to make this calculation we consider the teleparallel gravity analogs of the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz. We find that Einstein and Bergmann-Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau-Lifshitz complex does not. Energy density turns out to be non-vanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write $\\omega=1$ and $\\Xi^2=1$ in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz as obtained for ...

  18. Moduli and (un)attractor black hole thermodynamics

    NARCIS (Netherlands)

    Astefanesei, D.; Goldstein, K.D.; Mahapatra, S.

    2008-01-01

    We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of bla

  19. Attractor states, control parameters, and co-adaptation in instructed L2 inferential comprehension: a design-based research study of a critical reading intervention Estados atratores, parâmetros de controle, e co-adaptação no ensino da compreensão inferencial em L2: uma pesquisa design-based de intervenção de leitura crítica

    Directory of Open Access Journals (Sweden)

    Moisés Damián Perales Escudero

    2013-01-01

    Full Text Available Previous L1 and L2 research on inferential comprehension has tended to follow a quantitative orientation. By contrast, L2 research on critical reading is qualitative and tends to ignore inferences. This paper presents a qualitative, design-based study of a critical reading intervention focused on promoting generative rhetorical inferences and investigating co-adaptation and emergence of new meaning-making capacities. Complexity theory (CT constructs were used to research processes of co-adaptation between the participants' comprehension and the teacher-researcher's understanding of learning and instructional needs. Identification of attractor states and control parameters in classroom discourse were used to explore unpredicted factors influencing the participants' inferential comprehension and further refine the intervention. The results indicate that rhetorical genre knowledge acted as a control parameter driving the students' comprehension to attractor states characterized by implausible inferences, and that this knowledge explains the emergence of pragmatic meaning (rhetorical inferences from semantic meaning. The paper illustrates the usefulness of CT constructs in doing design-based research qualitatively in a manner that informs both theory and practice.As pesquisas anteriores em L1 e L2 sobre compreensão inferencial tendem a uma orientação quantitativa. Por outro lado, a pesquisa sobre leitura crítica em L2 é qualitativa e tende a ignorar as inferências. Este artigo apresenta um estudo qualitativo (design-based research sobre uma intervenção de leitura crítica com foco na promoção de geração de inferências retóricas, investigando a co-adaptação e a emergência de capacidades de produção de novos significados. Os construtos da teoria da complexidade foram usados ??para investigar processos de co-adaptação entre a compreensão de aprendizagem e necessidades instrucionais dos participantes e do professor pesquisador. A

  20. Nonresidential Crime Attractors and Generators Elevate Perceived Neighborhood Crime and Incivilities

    Science.gov (United States)

    McCord, Eric S.; Ratcliffe, Jerry H.; Garcia, R. Marie; Taylor, Ralph B.

    2007-01-01

    Recent studies have produced conflicting findings about the impacts of local nonresidential land uses on perceived incivilities. This study advances work in this area by developing a land-use perspective theoretically grounded in Brantingham and Brantingham's geometry of crime model in environmental criminology. That focus directs attention to…

  1. Multiple steady states, limit cycles and chaotic attractors in evolutionary games with Logit Dynamics

    NARCIS (Netherlands)

    C.H. Hommes; M.I. Ochea

    2010-01-01

    This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cy

  2. On the Number of Attractors of Positive and Negative Boolean Automata Circuits.

    OpenAIRE

    Demongeot, Jacques; Noual, Mathilde; Sené, Sylvain

    2010-01-01

    International audience In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain t...

  3. Estimation of dynamic properties of attractors observed in hollow copper electrode atmospheric pressure arc plasma system

    Indian Academy of Sciences (India)

    S Ghorul; S N Sahasrabudhe; P S S Murthy; A K Das; N Venkatramani

    2002-07-01

    Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics. It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a hollow copper electrode arc plasma torch. In this paper we present details of computations involved in the estimation process of various dynamic properties and show how they reflect chaotic behavior of arc root in the system.

  4. The Damaged Object: A "Strange Attractor" in the Dynamical System of the Mind

    Science.gov (United States)

    Shulman, Graham

    2010-01-01

    This article discusses the impact of the damaged object on the development and functioning of psychic life with particular reference to the sense of reality. The damaged object is of pivotal significance in Klein's and Winnicott's models of psychic development and experience in early infancy. A key dimension of the development and functioning of…

  5. The Use of Complexity Theory and Strange Attractors to Understand and Explain Information System Development

    Science.gov (United States)

    Tomasino, Arthur P.

    2013-01-01

    In spite of the best efforts of researchers and practitioners, Information Systems (IS) developers are having problems "getting it right". IS developments are challenged by the emergence of unanticipated IS characteristics undermining managers ability to predict and manage IS change. Because IS are complex, development formulas, best…

  6. Multistability and hidden attractors in a multilevel DC/DC converter

    DEFF Research Database (Denmark)

    Zhusubaliyev, Zhanybai T.; Mosekilde, Erik

    2015-01-01

    for the hidden set in most cases has been so complicated that special analytic and/or numerical techniques have been required to locate the set. By simulating the model of a multilevel DC/DC converter that operates in the regime of high feedback gain, the paper illustrates how pulse-width modulated control can...

  7. Urban School Reform and the Strange Attractor of Low-Risk Relationships

    Science.gov (United States)

    Beabout, Brian R.

    2010-01-01

    In the aftermath of Hurricane Katrina in 2005, school leaders in a newly decentralized school system reached out to external organizations for partnerships--a job that had previously resided in the central office. The necessity of these contacts and the quantity of newly independent schools make a unique context for studying how school leaders…

  8. Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle

    Science.gov (United States)

    Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C.; Downey, Mike J.; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A.; Bretschneider, Till; van der Horst, Gijsbertus T. J.; Delaunay, Franck; Rand, David A.

    2014-01-01

    Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer. PMID:24958884

  9. Convergence and attractors of augmented Lagrangian formulations in the dynamic analysis of multibody systems

    Science.gov (United States)

    Bustamante, D. A.; Kurdila, A. J.; Menon, R. G.

    1993-04-01

    The augmented Lagrangian formulation used in the dynamic analysis of multibody systems under holonomic constraints is presently found to exhibit fixed-step convergence, so that the approximate accelerations and Lagrange multipliers at a fixed time interval approach the exact accelerations and multipliers as the number of iterations becomes large. Also noted are a fixed time-interval rate of convergence inequality for the Lagrange multipliers, and corroborating empirical evidence for these analytical developments.

  10. Dynamical systems, attractors, and neural circuits [version 1; referees: 3 approved

    Directory of Open Access Journals (Sweden)

    Paul Miller

    2016-05-01

    Full Text Available Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

  11. Organisational values as "attractors of chaos": An emerging cultural change to manage organisational complexity

    OpenAIRE

    Shimon L. Dolan; Garc??a, Salvador; Diegoli, Samantha; Auerbach, Alan

    2000-01-01

    Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on ...

  12. State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes

    CERN Document Server

    von der Heydt, Anna S

    2016-01-01

    Equilibrium climate sensitivity is a frequently used measure to predict long-term climate change. However, both climate models and observational data suggest a rather large uncertainty on climate sensitivity (CS). The reasons for this include: the climate has a strong internal variability on many time scales, it is subject to a non-stationary forcing and it is, on many timescales, out of equilibrium with the changes in the radiative forcing. Palaeo records of past climate variations give insight into how the climate system responds to various forcings although care must be taken of the slow feedback processes before comparing palaeo CS estimates with model estimates. In addition, the fast feedback processes can change their relative strength and time scales over time. Consequently, another reason for the large uncertainty on palaeo climate sensitivity may be the fact that it is strongly state-dependent. Using a conceptual climate model, we explore how CS can be estimated from unperturbed and perturbed model t...

  13. Are attractors 'strange', or is life more complicated than the simple laws of physics?

    Science.gov (United States)

    Pogun, S

    2001-01-01

    Interesting and intriguing questions involve complex systems whose properties cannot be explained fully by reductionist approaches. Last century was dominated by physics, and applying the simple laws of physics to biology appeared to be a practical solution to understand living organisms. However, although some attributes of living organisms involve physico-chemical properties, the genetic program and evolutionary history of complex biological systems make them unique and unpredictable. Furthermore, there are and will be 'unobservable' phenomena in biology which have to be accounted for.

  14. Reactivation in working memory: an attractor network model of free recall.

    Directory of Open Access Journals (Sweden)

    Anders Lansner

    Full Text Available The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view.

  15. Flexibility and Attractors in Context: Family Emotion Socialization Patterns and Children's Emotion Regulation in Late Childhood

    NARCIS (Netherlands)

    Lunkenheimer, E.S.; Hollenstein, T.P.; Wang, J.; Shields, A.M.

    2012-01-01

    Familial emotion socialization practices relate to children's emotion regulation (ER) skills in late childhood, however, we have more to learn about how the context and structure of these interactions relates to individual differences in children's ER. The present study examined flexibility and attr

  16. Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors

    OpenAIRE

    Lozi, René

    2015-01-01

    17 pages, 19 figures International audience We propose a new mechanism for undersampling chaotic numbers obtained by the ringcoupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows thebuilding of a PRNG which passes all NIST Test.This new geometric undersampling is very effective for generating 2 parallel streams of pseudorandomnumbers, as we show, computing carefully their properties, up to sequences of 10^12consecutives iterates of the ring coupled mappin...

  17. Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system

    Science.gov (United States)

    Afraimovich, Valentin S.; Moses, Gregory; Young, Todd

    2016-05-01

    We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, O k , k=1,\\ldots,p , have two-dimensional unstable manifolds that contain orbits connecting each O k to the next two equilibrium points O k+1 and O k+2 in the chain ({{O}p+1}={{O}1} ). We show that the union of these equilibria and their unstable manifolds form a two-dimensional surface with a boundary that is homeomorphic to a cylinder if p is even and a Möbius strip if p is odd. If, further, each equilibrium in the chain satisfies a condition called ‘dissipativity’, then this surface is asymptotically stable.

  18. Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.

    Science.gov (United States)

    Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C; Downey, Mike J; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A; Bretschneider, Till; van der Horst, Gijsbertus T J; Delaunay, Franck; Rand, David A

    2014-07-01

    Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.

  19. Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction

    Science.gov (United States)

    Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi

    This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.

  20. (Un)attractor black holes in higher derivative AdS gravity

    OpenAIRE

    Astefanesei, D.; Banerjee, N.; Dutta, S.

    2008-01-01

    We investigate five-dimensional static (non-)extremal black hole solutions in higher derivative Anti-de Sitter gravity theories with neutral scalars non- minimally coupled to gauge fields. We explicitly identify the boundary counterterms to regularize the gravitational action and the stress tensor. We illustrate these results by applying the method of holographic renormalization to computing thermodynamical properties in several concrete examples. We also construct numerical extremal black ho...

  1. Recurrent motifs as resonant attractor states in the narrative field: a testable model of archetype.

    Science.gov (United States)

    Goodwyn, Erik

    2013-06-01

    At the most basic level, archetypes represented Jung's attempt to explain the phenomenon of recurrent myths and folktale motifs (Jung 1956, 1959, para. 99). But the archetype remains controversial as an explanation of recurrent motifs, as the existence of recurrent motifs does not prove that archetypes exist. Thus, the challenge for contemporary archetype theory is not merely to demonstrate that recurrent motifs exist, since that is not disputed, but to demonstrate that archetypes exist and cause recurrent motifs. The present paper proposes a new model which is unlike others in that it postulates how the archetype creates resonant motifs. This model necessarily clarifies and adapts some of Jung's seminal ideas on archetype in order to provide a working framework grounded in contemporary practice and methodologies. For the first time, a model of archetype is proposed that can be validated on empirical, rather than theoretical grounds. This is achieved by linking the archetype to the hard data of recurrent motifs rather than academic trends in other fields.

  2. Recurrent motifs as resonant attractor states in the narrative field: a testable model of archetype.

    Science.gov (United States)

    Goodwyn, Erik

    2013-06-01

    At the most basic level, archetypes represented Jung's attempt to explain the phenomenon of recurrent myths and folktale motifs (Jung 1956, 1959, para. 99). But the archetype remains controversial as an explanation of recurrent motifs, as the existence of recurrent motifs does not prove that archetypes exist. Thus, the challenge for contemporary archetype theory is not merely to demonstrate that recurrent motifs exist, since that is not disputed, but to demonstrate that archetypes exist and cause recurrent motifs. The present paper proposes a new model which is unlike others in that it postulates how the archetype creates resonant motifs. This model necessarily clarifies and adapts some of Jung's seminal ideas on archetype in order to provide a working framework grounded in contemporary practice and methodologies. For the first time, a model of archetype is proposed that can be validated on empirical, rather than theoretical grounds. This is achieved by linking the archetype to the hard data of recurrent motifs rather than academic trends in other fields. PMID:23750942

  3. Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay

    DEFF Research Database (Denmark)

    Zhusubaliyev, Z. T.; Mosekilde, Erik; Churilov, A. N.;

    2015-01-01

    The release of luteinizing hormone (LH) is driven by intermittent bursts of activity in the hypothalamic nerve centers of the brain. Luteinizing hormone again stimulates release of the male sex hormone testosterone (Te) and, via the circulating concentration of Te, the hypothalamic nerve centers...

  4. Analysis and control of complex dynamical systems robust bifurcation, dynamic attractors, and network complexity

    CERN Document Server

    Imura, Jun-ichi; Ueta, Tetsushi

    2015-01-01

    This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.

  5. Computer-Game Construction: A Gender-Neutral Attractor to Computing Science

    Science.gov (United States)

    Carbonaro, Mike; Szafron, Duane; Cutumisu, Maria; Schaeffer, Jonathan

    2010-01-01

    Enrollment in Computing Science university programs is at a dangerously low level. A major reason for this is the general lack of interest in Computing Science by females. In this paper, we discuss our experience with using a computer game construction environment as a vehicle to encourage female participation in Computing Science. Experiments…

  6. N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities

    CERN Document Server

    Ferrara, Sergio

    2008-01-01

    We analyze the Hessian matrix of the black hole potential of N=8, d=4 supergravity, and determine its rank at non-BPS critical points, relating the resulting spectrum to non-BPS solutions (with non-vanishing central charge) of N=2, d=4 magic supergravities and their ``mirror'' duals. We find agreement with the known degeneracy splitting of N=2 non-BPS spectrum of generic special Kahler geometries with cubic holomorphic prepotential. We also relate non-BPS critical points with vanishing central charge in N=2 magic supergravities to a particular reduction of the N=8, 1/8-BPS critical points.

  7. 18 CFR 1304.411 - Fish attractor, spawning, and habitat structures.

    Science.gov (United States)

    2010-04-01

    ... TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION OF... constructed of anchored brush piles, log cribs, and/or spawning benches, stake beds, vegetation, or rock...

  8. On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes

    OpenAIRE

    Cai, Rong-Gen; Cao, Li-Ming

    2007-01-01

    In this paper we elaborate on the relation between the entropy formula of Wald and the "entropy function" method proposed by A. Sen. For spherically symmetric extremal black holes, it is shown that the expression of extremal black hole entropy given by A. Sen can be derived from the general entropy definition of Wald, without help of the treatment of rescaling the AdS_2 part of near horizon geometry of extremal black holes. In our procedure, we only require that the surface gravity approaches...

  9. BOUNDARY CRISIS OF ATTRACTOR IN THE SIMULATION CAUSES OF THE DEGRADATION OF COMMERCIAL BIORESOURCES

    OpenAIRE

    A. Yu. Perevarukha

    2015-01-01

    The article describes the computational model that unites the formalization of ecological features of the reproductive cycle of anadromous fish and the possibility of studying nonlinear effects in the population dynamics under anthropogenic impact. Event-driven component implemented in continuous time has allowed us to take into account changes in the survival generation in interrelation with the factors of growth rate. Discrete component trajectory of the dynamical system has two areas of at...

  10. Shrimp trawlers as a local attractor of seabirds in nearshore waters of South Carolina, USA

    Science.gov (United States)

    Jodice, Patrick G.; Wickliffe, Lisa C.; Sachs, Elena B.

    2011-01-01

    Shrimp trawling is common throughout the southeastern and Gulf of Mexico coasts of the USA and is the primary contributor to fisheries discards in these regions. Tens of thousands of nearshore seabirds nest near shrimp trawling grounds in the USA, but to date, there has been no assessment of the relationship between seabirds and shrimp trawlers. We examined the taxonomic composition of bycatch, rate at which seabirds scavenged bycatch, and energy density of discarded bycatch in a nearshore commercial shrimp fishery. Bycatch was primarily comprised of demersal fish that are not typically accessible to the plunge-diving and surface-feeding seabirds that occur in the area. Hence, seabird diets in the region appear to be broadened taxonomically by the availability of discards. Results from discard experiments indicated that 70% of the nearly 5,500 items discarded by hand were scavenged by seabirds and that the fate of a discarded item was most strongly predicted by its taxonomic order. Laughing gulls scavenged the greatest proportion of discards, although brown pelicans were the only species to scavenge more discards than predicted based upon their abundance. Because this is the first such study in the region, it is difficult to ascertain the extent or intensity of the impact that discards have on nearshore seabirds. Nonetheless, our results suggest that it will be difficult for managers to clearly understand fluctuations in local seabird population dynamics without first understanding the extent to which these species rely upon discards. This may be especially problematic in situations where seabird populations are recovering following natural or anthropogenic stressors.

  11. Hydration Simulations of a Carbon Nanotube, Immersed in Water, according to the 3-Attractor Water Model

    Directory of Open Access Journals (Sweden)

    Francis F. Muguet

    2005-04-01

    Full Text Available MC simulations of a set of zigzag ((9,0-(14,0 and armchair ((6,6-(10,10carbon nanotubes immersed in water have been carried out in an NpT-ensemble (512 watermolecules, p=1 bar, T=298 K. Intermolecular interactions were described by BMWpotential according to which, besides the well-known linear water dimer bifurcated andinverted water dimers are metastable. In all cases, it was found that there are large periodicfluctuations of water occupancy inside the nanotubes. Decrease in the size of the nanotubediameter leads to a significant destruction of the H-bond network, and to a bifucarted dimerpopulation increase. Inverted dimer concentration relationship with the nanotube diameter ismore complicated. Population maximum for inverted dimers occurs for diameters of 10-11 å. Water features different intermolecular structures not only inside carbon nanotubesbut also in the outer first hydration shells. The amount of bifurcated and inverted dimers issignificantly more important in the first hydration shell than in bulk water.

  12. Symmetron and de Sitter attractor in a teleparallel model of cosmology

    CERN Document Server

    Sadjadi, H Mohseni

    2016-01-01

    In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via $Z_2$ symmetry breaking. While the conformal coupling holds the Universe in a vacuum with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at late time.

  13. RESEARCH ANNOUNCEMENTS Random Attractors for a Dissipative Quasi-geostrophic Dynamical System Under Stochastic Forcing%Random Attractors for a Dissipative Quasi-geostrophic Dynamical System Under Stochastic Forcing

    Institute of Scientific and Technical Information of China (English)

    黄代文

    2007-01-01

    @@ We consider the two-dimensional stochastic quasi-geostrophic equation[12p.234,13]((Э)/(Э)t+(Э)ψ/(Э)x(Э)/(Э)y-(Э)ψ/(Э)y(Э)/(Э)x)(△ψ-Fψ+β0y)=1/Re△2ψ-r/2△ψ+f(x,y,t) (1.1)on a regular bounded open domain D (С) R2,where ψis the stream function,F Froude Number (F≈O(1)),Re Reynolds number(Re≥102),β0a Positive constant(β0≈O(10-1)),r the Ekman dissipation constant(r≈O(1)),the external forcing term f(x,y,t)=-dW/dt(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the restrictions imposed below.

  14. The Role of the Positive and Negative Emotional Attractors in Vision and Shared Vision: Toward Effective Leadership, Relationships and Engagement

    OpenAIRE

    Richard Eleftherios Boyatzis; Kylie eRochford; Scott eTaylor

    2015-01-01

    Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of...

  15. The Norma Cluster (ACO 3627): I. A Dynamical Analysis of the Most Massive Cluster in the Great Attractor

    CERN Document Server

    Woudt, P A; Lucey, J; Fairall, A P; Moore, S A W

    2007-01-01

    A detailed dynamical analysis of the nearby rich Norma cluster (ACO 3627) is presented. From radial velocities of 296 cluster members, we find a mean velocity of 4871 +/- 54 km/s and a velocity dispersion of 925 km/s. The mean velocity of the E/S0 population (4979 +/- 85 km/s) is offset with respect to that of the S/Irr population (4812 +/- 70 km/s) by `Delta' v = 164 km/s in the cluster rest frame. This offset increases towards the core of the cluster. The E/S0 population is free of any detectable substructure and appears relaxed. Its shape is clearly elongated with a position angle that is aligned along the dominant large-scale structures in this region, the so-called Norma wall. The central cD galaxy has a very large peculiar velocity of 561 km/s which is most probably related to an ongoing merger at the core of the cluster. The spiral/irregular galaxies reveal a large amount of substructure; two dynamically distinct subgroups within the overall spiral-population have been identified, located along the Nor...

  16. Extended Fisher-Kolmogorov系统的渐近吸引子%Asymptotic attractor of Extended Fisher-Kolmogorov system

    Institute of Scientific and Technical Information of China (English)

    罗宏; 蒲志林

    2004-01-01

    考虑了Extended Fisher-Kolmogorov系统的解的长时间行为,构造了一个有限维解序列即该系统的渐近吸引子,证明了它在长时间后无限趋于方程的整体吸引子,并给出了渐近吸引子的维数估计.

  17. The role of the positive emotional attractor in vision and shared vision: toward effective leadership, relationships, and engagement

    OpenAIRE

    Boyatzis, Richard E.; Rochford, Kylie; Taylor, Scott N.

    2015-01-01

    Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of...

  18. Üner Tan Syndrome: Review and Emergence of Human Quadrupedalism in Self-Organization, Attractors and Evolutionary Perspectives

    OpenAIRE

    Tan, Üner; Tamam, Yusuf; Karaca, Sibel; Tan, Meliha

    2012-01-01

    The first man reported in the world literature exhibiting habitual quadrupedal locomotion was discovered by a British traveler and writer on the famous Baghdat road near Havsa/Samsun on the middle Black-Sea coast of Turkey (Childs, 1917). Interestingly, no single case with human quadrupedalism was reported in the scientific literature after Child's first description in 1917 until the first report on the Uner Tan syndrome (UTS: quadrupedalism, mental retardation, and impaired speech or no spee...

  19. F center in sodium electrosodalite as a physical manifestation of a non-nuclear attractor in the electron density

    Science.gov (United States)

    Madsen, G. K. H.; Gatti, C.; Iversen, B. B.; Damjanovic, Lj.; Stucky, G. D.; Srdanov, V. I.

    1999-05-01

    The structure of sodium electrosodalite (SES), Na8(AlSiO4)6, has been determined at 20 K using synchrotron powder diffraction. Subsequently the electron density was calculated through a periodic unrestricted Hartree-Fock approach and analyzed by topological methods. The F center is found to manifest itself as a maximum in the electron density at a non-nuclear position. Thus it possesses a separate identity and behaves quantum mechanically as an open system, bounded by a surface of local zero flux in the gradient vector field of the electron density. Different basis sets have been considered, and the introduction of a basis set capable of describing the F center leads to a large drop in the total energy. The F center contains almost solely unpaired electron density which is loosely bound and exhibits a very low kinetic energy density. Calculations on both a ferromagnetic and an antiferromagnetic phase have been performed and the total electron densities in the two phases are found to be very similar, with the alternating ordering of the spin density being the only difference between the two phases. The electron localization function has been introduced for an open-shell system and has been used to illustrate the magnetic phase transition.

  20. Alternation of up and down states at a dynamical phase-transition of a neural networkwith spatiotemporal attractors

    Directory of Open Access Journals (Sweden)

    Silvia eScarpetta

    2014-05-01

    Full Text Available Complex collective activity emerges spontaneously in cortical circuits in-vivo and in-vitro, such as alternation of up and down states, precise spatiotemporal patterns replay, and power law scaling of neural avalanches. We focus on such critical features observed in cortical slices.We study spontaneous dynamics emerging in noisy recurrent networks of spiking neurons with sparse structured connectivity.The emerging spontaneous dynamics is studied, in presence of noise, with fixed connections. Note that no short-term synaptic depression is used. Two different regimes of spontaneous activity emerge changing the connection strength or noise intensity: a low activity regime, characterized by a nearly exponential distribution of firing rates with a maximum at rate zero, and a high activity regime, characterized by a nearly Gaussian distribution peaked at a high rate for high activity, with long-lasting replay of stored patterns. Between this two regimes, a transition region is observed, where firing rates show a bimodal distribution, with alternation of up and down states. In this region, one observes neuronal avalanches exhibiting power laws in size and duration, and a waiting time distribution between successive avalanches which shows a non-monotonic behaviour. During periods of high activity (up states consecutive avalanches are correlated, since they are part of a short transient replay initiated by noise focusing, and waiting times show a power law distribution. One can think at this critical dynamics as a reservoire of dynamical patterns for memory functions.

  1. Multiple attractors and critical parameters and how to find them numerically: the right, the wrong and the gambling way

    DEFF Research Database (Denmark)

    True, Hans

    2013-01-01

    In recent years, several authors have proposed easier numerical methods to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are comme......In recent years, several authors have proposed easier numerical methods to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras...

  2. On multiple attractors and critical parameters and how to find them numerically: The right, the wrong and "the American way"

    DEFF Research Database (Denmark)

    True, Hans

    2011-01-01

    In recent years several authors have proposed, "easier" numerical methods' to find the critical speed in railway dynamical problems. Actually the methods do function in some cases, but in most cases it is really a gamble. In this presentation the methods will be discussed and the pros and contras...

  3. On the Parallel Between Zipf's Law and 1/f Processes\\in Chaotic Systems Possessing Coexisting Attractors --A Possible Mechanism for language Formation in the Cerebral Cortex--

    Science.gov (United States)

    Nicolis, J. S.; Tsuda, I.

    1989-08-01

    A chaotic dynamics model of creating Markovian strings of symbols as well as sequences of "words" is exposed, and its relevance to Zipf's law in experimental linguistics is discussed. Recent developments of brain science and linguistics suggest a preliminary theory of language formation by means of chaotic dynamics both in groups of cerebral neurons and the thalamocortical pacemaker itself.

  4. Numerical and experimental studies of attractors in memristor-based Chua's oscillator with a line of equilibria. Noise-induced effects

    Science.gov (United States)

    Semenov, V.; Korneev, I.; Arinushkin, P.; Strelkova, G.; Vadivasova, T.; Anishchenko, V.

    2015-07-01

    The intrinsic features of systems with a line of equilibria are analyzed by studying of memristor-based Chua's oscillator. The analog modeling of the system is carried out together with its numerical simulation. The characteristics of stochastic oscillations in the system under study are explored in the presence of noise. The issues concerning the physical realization of a system with a line of equilibria are also considered.

  5. Global Attractor for Complex Ginzburg Landau Equation in Whole R3%三维全空间上Ginzburg-Landau方程的整体吸引子

    Institute of Scientific and Technical Information of China (English)

    李栋龙; 郭柏灵

    2004-01-01

    作者在三维全空间中考虑研究复Ginzburg-Landau方程(CGL)的解的长时间行为.通过引入权空间,应用内插不等式和在权空间的先验估计,获得复 Ginzburg-Landau方程整体解的存在性,进一步建立了整体吸引子的存在性.

  6. Real Projective Iterated Function Systems

    CERN Document Server

    Barnsley, Michael F; Wilson, David C

    2010-01-01

    This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to connections between attractors that avoid hyperplanes and repellers that avoid points as well as hyperplane attractors that avoid points and repellers that avoid hyperplanes. Finally, an index is defined for attractors which avoid a hyperplane. This index is shown to be a nontrivial projective invariant.

  7. Introduction to semiflows

    CERN Document Server

    Milani, Albert J

    2004-01-01

    DYNAMICAL PROCESSESIntroductionOrdinary Differential EquationsAttracting SetsIterated SequencesLorenz' EquationsDuffing's EquationSummaryATTRACTORS OF SEMIFLOWSDistance and SemidistanceDiscrete and Continuous SemiflowsInvariant SetsAttractorsDissipativityAbsorbing Sets and AttractorsAttractors via a-ContractionsFractal DimensionA Priori EstimatesATTRACTORS FOR SEMILINEAR EVOLUTION EQUATIONSPDEEs as Dynamical SystemsFunctional FrameworkThe Parabolic ProblemThe Hyperbolic ProblemRegularityUpper Semicontinuity of the Global AttractorsEXPONENTIAL ATTRACTORSIntroductionThe Discrete Squeezing Proper

  8. THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION

    Institute of Scientific and Technical Information of China (English)

    Liu Yingdong; Li Zhengyuan

    2000-01-01

    We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.

  9. 基于径向基函数网络的混沌吸引子寻找方法%The Method of Looking for Chaotic Attractor Based on Radial Basis Function Networks

    Institute of Scientific and Technical Information of China (English)

    向小东

    2004-01-01

    由于现有的混沌吸引子识别方法对噪声敏感,研究带噪声的时间序列的混沌识别方法就显得特别重要.本文给出了一种新的基于径向基函数网络的混沌吸引子寻找方法.实例表明此方法对即使少量的、噪声较大的时间序列也有较好的效果,是一种很实用的方法,有着广阔的应用前景.

  10. Uniform Attractors for the Viscoelastic Equation with a Nonlinear Boundary Damping (Ⅰ)%具有非线性阻尼粘弹方程的一致吸引子(Ⅰ)

    Institute of Scientific and Technical Information of China (English)

    秦玉明; 胡阳艳; 刘震宇; 袁亚波; 安晶晶; 周奥

    2014-01-01

    吸引子的存在性问题是无穷维动力系统的主要问题之一.在本文中,建立了有非线性边界阻尼均匀流动的粘弹性方程,通过能量衰减和建立李雅普诺夫函数,最后,证明了吸引子的存在.

  11. 一类模式演化方程的全局吸引子及其维数估计%Global Attractors for a Class of Pattern Formation Equations

    Institute of Scientific and Technical Information of China (English)

    张天佑; 穆春来; 邢庭莉

    2007-01-01

    研究了一类源自模式演化问题的非线性发展方程所产生的动力系统,并考虑了其全局吸引子的存在性及维数估计问题.这类模式演化方程与化学反应和火焰燃烧有密切关系,因此具有重要的物理背景,而且因为它含有关于空间变量的四阶微分算子,还具有重要的理论价值.借助插值不等式以及sobolev嵌入定理,可以进行一系列精细的估计,最终根据一个经典的结果,证明了在维数不超过三维的空间中的有界集合上,系统的全局吸引子存在.进一步应用Sobolev-Lieb-Thirring不等式进行估计,可以得到全局吸引子的分形维数的界.

  12. A Class of Iterated Function Systems with Two Parameters and Their Attractors%一类具有双参数的迭代函数系及其吸引子

    Institute of Scientific and Technical Information of China (English)

    王宏勇

    2007-01-01

    基于Barnsley的分形构造法,构造了一类具有双参数的非线性迭代函数系.与传统的线性迭代函数系相比,所构造的迭代函数系具有更高的灵活性,它的吸引子即分形插值曲线能更好地拟合实验数据.证明了这类分形插值函数关于双参数是Lipschitz连续的,并讨论了这类分形插值曲线的参数界定问题,最后给出了关于双参数的充分条件.为图象压缩和数据拟合等实际应用提供了理论基础.

  13. Two-Layer Feedback Neural Networks with Associative Memories

    Institute of Scientific and Technical Information of China (English)

    WU Gui-Kun; ZHAO Hong

    2008-01-01

    We construct a two-layer feedback neural network by a Monte Carlo based algorithm to store memories as fixed-point attractors or as limit-cycle attractors. Special attention is focused on comparing the dynamics of the network with limit-cycle attractors and with fixed-point attractors. It is found that the former has better retrieval property than the latter. Particularly, spurious memories may be suppressed completely when the memories are stored as a long-limit cycle. Potential application of limit-cycle-attractor networks is discussed briefly.

  14. Variations of Boundary Surface in Chua’s Circuit

    Directory of Open Access Journals (Sweden)

    M. Guzan

    2015-09-01

    Full Text Available The paper compares the boundary surfaces with help of cross-sections in three projection planes, for the four changes of Chua’s circuit parameters. It is known that due to changing the parameters, the Chua’s circuit can be characterized in addition to a stable limit cycle also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua’s circuit can even start working as a binary memory. It is not known yet, how changes in parameters and conseqently in attractors in the circuit will affect the morphology of the boundary surface. The boundary surface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper the boundary surface will separate even single scroll chaotic attractors from each other. Dividing the state space into regions of attractivity for different attractors, however, remains fundamentally the same.

  15. A new multi-scroll chaotic system

    Institute of Scientific and Technical Information of China (English)

    Wang Fa-Qiang; Liu Chong-Xin

    2006-01-01

    This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors.The characteristic of this new multi-scroll chaotic system is that the 4n + 2m +4-scroll chaotic attractors are generated easily with n and m varying under n ≤ m. Various number of scroll chaotic attractors are illustrated not on ly by computer simulation but also by the realization of an electronic circuit experiment on EWB (Electronics Workbench).

  16. Chaotic itinerancy and its roles in cognitive neurodynamics

    OpenAIRE

    Tsuda, Ichiro

    2015-01-01

    Chaotic itinerancy is an autonomously excited trajectory through high-dimensional state space of cortical neural activity that causes the appearance of a temporal sequence of quasi-attractors. A quasi-attractor is a local region of weakly convergent flows that represent ordered activity, yet connected to divergent flows representing disordered, chaotic activity between the regions. In a cognitive neurodynamic aspect, quasi-attractors represent perceptions, thoughts and memories, chaotic traje...

  17. Canonical self-affine tilings by iterated function systems

    OpenAIRE

    Pearse, Erin P. J.

    2006-01-01

    An iterated function system $\\Phi$ consisting of contractive similarity mappings has a unique attractor $F \\subseteq \\mathbb{R}^d$ which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling $\\mathcal{T}$ of the convex hull of the attractor. More precisely, it tiles the complement of the attractor within its convex hull. These tiles form a collection of sets whose geometry is typically ...

  18. Coalescence in coupled Duffing oscillators

    Institute of Scientific and Technical Information of China (English)

    YANG Jun-Zhong

    2009-01-01

    The forced Duffing oscillator has a pair of symmetrical attractors in a proper parameter regime. When a lot of Duffing oscillators are coupled linearly, the system tends to form clusters in which the neighboring oscillators fall onto the same attractor. When the coupling strength is strong, all of the oscillators fall onto one attractor. In this work, we investigate coalescence in the coupled forced Duffing oscillators. Some phenomena are found and explanations are presented.

  19. Dynamics of Generalized Tachyon Field in Teleparallel Gravity

    OpenAIRE

    Behnaz Fazlpour; Ali Banijamali

    2014-01-01

    We study dynamics of generalized tachyon scalar field in the framework of teleparallel gravity. This model is an extension of tachyonic teleparallel dark energy model which has been proposed by Banijamali and Fazlpour (2012). In contrast with tachyonic teleparallel dark energy model that has no scaling attractors, here we find some scaling attractors which means that the cosmological coincidence problem can be alleviated. Scaling attractors are presented for both interacting and noninteractin...

  20. NUMERICAL ANALYSIS OF A CHAOTIC SYSTEM

    Institute of Scientific and Technical Information of China (English)

    任志坚

    2001-01-01

    This paper further proves that a single spiral strange attractor can be observed in an extremely simple autonomous electrical circuit by computer simulation. It is of third order and has only one nonlinear element: a three-segment piecewise linear resistor. The digital analyses show that the strange attractor has peculiar features compared with other third-order differential systems.

  1. THE LONG TIME BEHAVIORS OF NON-AUTONOMOUS EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW WITHIN THE EARTH

    Institute of Scientific and Technical Information of China (English)

    ZHAO Chunshan; LI Kaitai; HUANG Aixiang

    2002-01-01

    In this paper, the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied. The uniqueness and existence of the solution to the evolution system and the existence of uniform attractor are proven.Moreover, the upper bounds of the uniform attractor's Hausdorff and Fractal dimensions are obtained.

  2. Chaos as a part of logical structure in neurodynamics

    Science.gov (United States)

    Zak, Michail

    1989-01-01

    It is proposed that chaotic attractors incorporated in neural net models can represent classes of patterns in the same way in which a set of static attractors represent unrelated patterns. Therefore, chaotic states of neuron activity are associated with higher level cognitive processes such as generalization and abstraction.

  3. THE LONG TIME BEHAVIORS OF NON-AUTONOMOUS EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW WITHIN THE

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    In this paper,the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied.The uniqueness and existence of the solution to the evolution system and the existence of uniform attractor are proven.Moreover,the upper bounds of the uniform attractor's hausdorff and Fractal dimensions are obtained.

  4. Chaos and quasi-periodicity in diffeomorphisms of the solid torus

    NARCIS (Netherlands)

    Broer, H.W.; Simó, C.; Vitolo, R.

    2010-01-01

    This paper focuses on the parametric abundance and the 'Cantorial' persistence under perturbations of a recently discovered class of strange attractors for diffeomorphisms, the so-called quasi-periodic Henon-like. Such attractors were first detected in the Poincare map of a periodically driven model

  5. Long-term Analysis of Degenerate Parabolic Equations in RN

    Institute of Scientific and Technical Information of China (English)

    Gao Cheng YUE; Cheng Kui ZHONG

    2015-01-01

    Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using ?-trajectories methods, we proved that weak solutions generated by degenerate equations possess an (L2U (RN ), L2loc(RN ))-global attractor. Moreover, the upper bounds of the Kolmogorovε-entropy for such global attractor are also obtained.

  6. Asymptotic behavior of a delay predator-prey system with stage structure and variable coefficients

    Directory of Open Access Journals (Sweden)

    Javier A. Hernandez-Pinzon

    2008-10-01

    Full Text Available In this paper, we establish a global attractor for a Lotka-Volterra type reaction-diffusion predator-prey model with stage structure for the predator, delay due to maturity and variable coefficients. This attractor is found by the method of upper and lower solutions and is given in terms of bounds for the coefficients.

  7. Approximation of the Long-term Dynamics of the Dynamical System Generated by the Two-dimensional Thermohydraulics Equations

    CERN Document Server

    Tone, Florentina

    2011-01-01

    Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

  8. Analysis of stochastic effects in Kaldor-type business cycle discrete model

    Science.gov (United States)

    Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna

    2016-07-01

    We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions "chaos-order" is discussed.

  9. Experimental Confirmation of a Modified Lorenz System

    Institute of Scientific and Technical Information of China (English)

    LIU Ling; LIU Chong-Xin; ZHANG Yan-Bin

    2007-01-01

    We experimentally demonstrate the butterfly-shaped chaotic attractor we have proposed before [Int. J. Nonlin.Sci. Numerical Simulation 7 (2006) 187]. Some basic dynamical properties and chaotic behaviour of this new butterfly attractor are studied and they are in agreement with the results of our theoretical analysis. Moreover,the proposed system is experimental demonstrated.

  10. GLOBAL SOLUTION AND ITS LONG TIME BEHAVIOR FOR THE GENERALIZED LONG-SHORT WAVE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Zhang Ruifeng; Guo Boling

    2005-01-01

    The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.

  11. LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHR(O)DINGER EQUATION WITH WEAKLY DAMPED

    Institute of Scientific and Technical Information of China (English)

    Fa-yong Zhang

    2004-01-01

    The three-dimensional nonlinear Schrodinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.

  12. SLYRB measures : natural invariant measures for chaotic systems

    NARCIS (Netherlands)

    Hunt, BR; Kennedy, JA; Li, TY; Nusse, HE

    2002-01-01

    In many applications it is useful to consider not only the set that constitutes an attractor but also (if it exists) the asymptotic distribution of a typical trajectory converging to the attractor. Indeed, in the physics literature such a distribution is often assumed to exist. When it exists, it is

  13. Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

    Science.gov (United States)

    Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

    2015-10-01

    The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

  14. Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

    Energy Technology Data Exchange (ETDEWEB)

    Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp [Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601 (Japan); Yamada, Michio [Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502 (Japan); Chian, Abraham C.-L. [Paris Observatory, LESIA, CNRS, 92195 Meudon (France); National Institute for Space Research (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010 (Brazil); Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil); School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005 (Australia); Department of Biomedical Engineering, George Washington University, Washington, DC 20052 (United States); Miranda, Rodrigo A. [Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, University of Brasília (UnB), Brasília DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)

    2015-10-15

    The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

  15. Extreme multistability in a memristor-based multi-scroll hyper-chaotic system.

    Science.gov (United States)

    Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

    2016-07-01

    In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

  16. Extreme multistability in a memristor-based multi-scroll hyper-chaotic system

    Science.gov (United States)

    Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

    2016-07-01

    In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

  17. Archetypal oscillator for smooth and discontinuous dynamics

    Science.gov (United States)

    Cao, Qingjie; Wiercigroch, Marian; Pavlovskaia, Ekaterina E.; Grebogi, Celso; T. Thompson, J. Michael

    2006-10-01

    We propose an archetypal system to investigate transitions from smooth to discontinuous dynamics. In the smooth regime, the system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. At the discontinuous limit, however, there is a substantial departure in the dynamics from the standard one. In particular, the velocity flow suffers a jump in crossing from one well to another, caused by the loss of local hyperbolicity due to the collapse of the stable and unstable manifolds of the stationary state. In the presence of damping and external excitation, the system has coexisting attractors and also a chaotic saddle which becomes a chaotic attractor when a smoothness parameter drops to zero. This attractor can bifurcate to a high-period periodic attractor or a chaotic sea with islands of quasiperiodic attractors depending on the strength of damping.

  18. A Cayley Tree Immune Network Model with Antibody Dynamics

    CERN Document Server

    Anderson, R W; Perelson, A S; Anderson, Russell W.; Neumann, Avidan U.; Perelson, Alan S.

    1993-01-01

    Abstract: A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analyzed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters, percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percola...

  19. Laboratory Tests of the Inverse Square Law of Gravity

    Science.gov (United States)

    Schlamminger, Stephan

    2010-02-01

    Newton's inverse square force law of gravity follows directly from the fact that we live in a 3-dimensional world. For sub-millimeter length scales there may be undiscovered, extra dimensions. Such extra dimensions can be detected with inverse square law tests accessible to torsion balances. I will present an overview of two experiments that are being conducted at the University of Washington to search for gravitational-strength deviations from the inverse square law for extra dimension length scales smaller than 50 micrometers. One experiment is designed to measure the distance dependent force between closely spaced masses, whereas the second experiment is a null experiment and is only sensitive to a deviation from the inverse square law of gravity. The first experiment consists of a torsion pendulum that is suspended above a continuously rotating attractor. The attractor and the pendulum are disks with azimuthal sectors of alternating high and a low density. The torque on the pendulum disk varies as a function of the attractor angle with a 3 degree period. The amplitude of the torque signal is analyzed as a function of the separation between the pendulum and the attractor. The second experiment consists of a plate pendulum that is suspended parallel to a larger vertical plate attractor. The pendulum plate has an internal density asymmetry with a dense inlay on one half facing the attractor and another inlay on the other half on the side away from the attractor. If the inverse square law holds, the gravitational field of the attractor is uniform and the torque on the pendulum is independent of the gap between pendulum and attractor. The attractor position is modulated between a near and far position and the torque difference on the pendulum is recorded and analyzed for a possible inverse square law violation. )

  20. 一维线性热弹系统的整体解存在性、渐近性和一致吸引子%Global Existence, Asymptotic Behavior and Uniform Attractor for a One-Dimensional Linear Thermoelastic System

    Institute of Scientific and Technical Information of China (English)

    秦玉明; 王鹏达; 陈艳芳

    2015-01-01

    考虑了一维线性热弹系统.这个系统包含了一个波方程和一个热方程.通过运用半群方法和多乘子方法,建立了解的整体存在性和渐近性,并通过一致压缩函数的方法进一步证明了一个非自治热弹系统一致吸引子的存在性.