Random Attractors: Robustness, Numerics and Chaotic Dynamics

Gunter Ochs
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Gunter Ochs: Universität Bremen, Institut für Dynamische Systeme

A chapter in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 2001, pp 1-30 from Springer

Abstract: Abstract In this article the numerical approximation of attractors and invariant measures for random dynamical systems by using a box covering algorithm is discussed. We give a condition under which the algorithm, which defines a set valued random dynamical system, possesses an attractor close to the attractor of the original system. Furthermore, a general existence theorem for attractors for set valued random dynamical systems is proved and criteria for the robustness of random attractors under perturbations of the system are given. Our numerical algorithm is applied to the stochastically forced Duffing oscillator, which supports for certain parameter values a non trivial random SRB measure.

Keywords: Markov Process; Lyapunov Exponent; Invariant Measure; Chaotic Dynamics; Unstable Manifold (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56589-2_1

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DOI: 10.1007/978-3-642-56589-2_1

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