Finite fractal dimensions of random attractors for stochastic FitzHugh-Nagumo system with multiplicative white noise

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Zhou, Shengfan¹  Wang, Zhaojuan² 

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China

关键词: Stochastic FitzHugh-Nagumo system;    Random attractor;    Multiplicative white noise;    Fractal dimension;    Random dynamical system;   

DOI  :  10.1016/j.jmaa.2016.04.038

来源: Elsevier

【 摘 要 】

In this paper, we consider the asymptotic behavior of solutions for stochastic non autonomous FitzHugh-Nagumo system with multiplicative white noise. First we prove the existence of random attractor of the random dynamical system generated by the solutions of considered system. Then we present some conditions for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space and apply these conditions to prove the finiteness of fractal dimension of random attractor. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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