Strange Nonchaotic Attractors in Random Dynamical Systems [PDF]
Physical Review Letters, 2004 Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time ...
Wang, X. +3 more
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Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain
Journal of Inequalities and Applications, 2016 In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings.
CX Guo, YY Chen, YF Guo
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Random Attractor for Stochastic Wave Equation with Arbitrary Exponent and Additive Noise on $\mathbb{R}^n$ [PDF]
, 2014 Asymptotic random dynamics of weak solutions for a damped stochastic wave equation with the nonlinearity of arbitrarily large exponent and the additive noise on $\mathbb{R}^n$ is investigated.
Li, Hongyan, You, Yuncheng
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Random sampling vs. exact enumeration of attractors in random Boolean networks [PDF]
, 2009 We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs).
Aldana M +9 more
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The random case of Conley's theorem
, 2005 The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e.
Arnold L +12 more
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Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also ...
Shangzhi Li, Shangjiang Guo
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Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system
, 2005 To study a chaotic itinerant motion among varieties of ordered states, we propose a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line, and a Markov chain with a transition probability matrix.
F. Spitzer +4 more
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Regular Attractor by Strict Lyapunov Function for Random Dynamical Systems
Wasit Journal for Pure SciencesThe main objective of this paper is to study some types of random attractors in random dynamical systems based on the random strict Lyapunov function.
Hind Adnan Hashim
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Asymptotic behaviour of random tridiagonal Markov chains in biological applications
, 2012 Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors.
A. E. Hutzenthaler +21 more
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The effect of Hebbian plasticity on the attractors of a dynamical system [PDF]
, 2008 Poster presentation A central problem in neuroscience is to bridge local synaptic plasticity and the global behavior of a system. It has been shown that Hebbian learning of connections in a feedforward network performs PCA on its inputs [1]. In recurrent
Zhu, Junmei
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