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Random Attractors: Robustness, Numerics and Chaotic Dynamics

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

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  • Gunter Ochs

    (Universität Bremen, Institut für Dynamische Systeme)

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.

Suggested Citation

  • Gunter Ochs, 2001. "Random Attractors: Robustness, Numerics and Chaotic Dynamics," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 1-30, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_1
    DOI: 10.1007/978-3-642-56589-2_1
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