Approximation of invariant foliations for stochastic dynamical systems

Xu Sun, Xingye Kan, Jinqiao Duan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random sets. Thus it is desirable to have some techniques to approximate random invariant foliations. In this paper, invariant foliations are approximated for dynamical systems with small noisy perturbations, via asymptotic analysis. Namely, random invariant foliations are represented as a perturbation of the deterministic invariant foliations, with deviation errors estimated.

Original languageEnglish (US)
Article number1150011
JournalStochastics and Dynamics
Volume12
Issue number1
DOIs
StatePublished - Mar 1 2012

Keywords

  • SDEs
  • SPDEs
  • Stable and unstable foliations
  • asymptotic expansion
  • fiber or leaf
  • fluctuations
  • random dynamical systems

Fingerprint Dive into the research topics of 'Approximation of invariant foliations for stochastic dynamical systems'. Together they form a unique fingerprint.

Cite this