Identifying almost invariant sets in stochastic dynamical systems

Lora Billings, Ira B. Schwartz

17 Scopus citations

Abstract

We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius-Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered.

Original languageEnglish
Article number023122
JournalChaos
Volume18
Issue number2
DOIs
Publication statusPublished - 2008

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