R3上带乘法噪声的非自治随机FitzHugh-Nagumo系统的随机指数吸引子

Abstract

Abstract:

The article considers the existence of a random exponential attractor (positive invariant compact measurable set with finite fractal dimension and attracting orbits exponentially) for non-autonomous stochastic FitzHugh-Nagumo system in R³, which deduces that the long-term behavior of solutions of system can be characterized by finite independent parameters. The proof is based on the "tail" estimation of solutions of systems and decomposing the difference of two solutions into three parts that one part belongs to finite-dimensional space and both of other two parts become small enough when both time variable and space variable are large enough.

Key words: Non-autonomous stochastic FitzHugh-Nagumo system, Random exponential attractor, Multiplicative white noise, Fractal dimension

CLC Number:

Zongfei Han,Shengfan Zhou. Random Exponential Attractor for Non-Autonomous Stochastic FitzHugh-Nagumo System with Multiplicative Noise in R³[J].Acta mathematica scientia,Series A, 2020, 40(3): 756-783.

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Random Exponential Attractor for Non-Autonomous Stochastic FitzHugh-Nagumo System with Multiplicative Noise in R³

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Random Exponential Attractor for Non-Autonomous Stochastic FitzHugh-Nagumo System with Multiplicative Noise in R³