Approximation of invariant foliations for stochastic dynamical systems

Xu Sun; Xingye Kan; Jinqiao Duan

doi:10.1142/S0219493712003614

Approximation of invariant foliations for stochastic dynamical systems

Xu Sun, Xingye Kan, Jinqiao Duan

Research output: Contribution to journal › Article › peer-review

7 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 language	English (US)
Article number	1150011
Journal	Stochastics and Dynamics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1142/S0219493712003614
State	Published - Mar 2012
Externally published	Yes

Bibliographical note

Funding Information:
Part of this work was done while J. Duan was participating the Stochastic Partial Differential Equations program at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. This work was partly supported by NSF of China grants 10971225 and 11028102, the NSF Grants 1025422 and 0731201, the Fundamental Research Funds for the Central Universities-HUST 2010ZD037, and an open research grant from the State Key Laboratory for Nonlinear Mechanics at the Chinese Academy of Sciences.

Keywords

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

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10.1142/S0219493712003614

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KW - asymptotic expansion

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KW - fluctuations

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Approximation of invariant foliations for stochastic dynamical systems

Abstract

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