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Random Point Attractors Versus Random Set Attractors [PDF]

Journal of the London Mathematical Society, 2001
Summary: The notion of an attractor for a random dynamical system with respect to a general collection of deterministic sets is introduced. This comprises, in particular, global point attractors and global set attractors. After deriving a necessary and sufficient condition for existence of the corresponding attractors it is proved that a global set ...
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Attractors for random dynamical systems

Probability Theory and Related Fields, 1994
Random dynamical systems are treated, the notions of an omega limit set, a random invariant set, an absorbing set and a global attractor are introduced. Conditions are given under which a global attractor (being a compact random invariant set) exists, and some of its properties are established.
FLANDOLI FRANCO, Hans Crauel
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Nonautonomous and Random Attractors

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2015
The theories of nonautonomous and random dynamical systems have undergone extensive, often parallel, developments in the past two decades. In particular, new concepts of nonautonomous and random attractors have been introduced. These consist of families of sets that are mapped onto each other as time evolves and have two forms: a forward attractor ...
Peter E. Kloeden, Peter E. Kloeden, Hans Crauel   +2 more
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On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise

Stochastics and Dynamics, 2017
Wong–Zakai type approximation for stochastic partial differential equations (abbreviate as PDEs) is well studied. Besides the polygonal approximation, a type of smooth noise approximation is considered. After showing the existence of random attractor for
Hongbo Fu, Xianming Liu, Jicheng Liu, Xiangjun Wang   +3 more
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Random Perturbations of Heteroclinic Attractors

SIAM Journal on Applied Mathematics, 1990
Estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation, subject to small additive random noise. The theory presented is illustrated with numerical simulations of several systems, including ones invariant under symmetry groups, for ...
Peter J. Holmes, Emily Stone
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Morse decompositions of uniform random attractors

Journal of Differential Equations, 2021
Abstract In this paper, we study the Morse theory on uniform random attractors for non-autonomous random dynamical systems. To handle the non-invariance of uniform random attractors, we construct the Morse sets of uniform random attractor as the projections of the Morse sets on pullback attractor of the skew product semiflow.
Xiaofang Lin, Caibin Zeng
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A uniformly exponential random forward attractor which is not a pullback attractor

Archiv der Mathematik, 2002
The author constructs an example of a random forward attractor for a random dynamical system (RDS) that is not a pullback attractor which is one of 3 possible notions of an attractor one can naturally define for RDS (and which all coincide for deterministic dynamical systems).
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Numerical Approximation of Random Attractors

2007
In this article an algorithm for the numerical approximation of random attractors based on the subdivision algorithm of Dellnitz and Hohmann is presented. It is applied to the stochastic Duffing-van der Pol oscillator, for which we also prove a theoretical result on the existence of stable/unstable manifolds and attractors. This system serves as a main
Hannes Keller, Gunter Ochs
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Random Attractor, Invariant Measures, and Ergodicity of Lattice p-Laplacian Equations Driven by Superlinear Noise

Journal of Geometric Analysis, 2023
Pengyu Chen, M. Freitas, Xuping Zhang
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Random Walk on a Strange Attractor

Physical Review Letters, 1984
On etudie les proprietes de transport des attracteurs etranges a l'aide d'une marche de sauterelle a sauts aleatoire sur des points separes d'une distance a±sa sur l ...
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