# American Institute of Mathematical Sciences

December  2016, 9(6): 1701-1715. doi: 10.3934/dcdss.2016071

## Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation

 1 School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China, China 2 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  June 2015 Revised  September 2016 Published  November 2016

Random invariant manifolds are considered for a stochastic Swift-Hohenberg equation with multiplicative noise in the Stratonovich sense. Using a stochastic transformation and a technique of cut-off function, existence of random invariant manifolds and attracting property of the corresponding random dynamical system are obtained by Lyaponov-Perron method. Then in the sense of large probability, an approximation of invariant manifolds has been investigated and this is further used to describe the geometric shape of the invariant manifolds.
Citation: Yanfeng Guo, Jinqiao Duan, Donglong Li. Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1701-1715. doi: 10.3934/dcdss.2016071
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