Document Type
Article
Publication Date
1-18-2008
Journal / Book Title
Chaos: An Interdisciplinary Journal of Nonlinear Science
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. © 2008 American Institute of Physics.
DOI
10.1063/1.2929748
MSU Digital Commons Citation
Billings, Lora and Schwartz, Ira, "Identifying almost invariant sets in stochastic dynamical systems" (2008). Department of Mathematics Facuty Scholarship and Creative Works. 18.
https://digitalcommons.montclair.edu/mathsci-facpubs/18
Published Citation
Billings, L., & Schwartz, I. B. (2008). Identifying almost invariant sets in stochastic dynamical systems. Chaos, 18(2), 023122. doi: 10.1063/1.2929748