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

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 756-783.

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

韩宗飞,周盛凡*()

^{浙江师范大学数学与计算机科学学院浙江金华 321004}

收稿日期:2019-03-29 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 周盛凡 E-mail:zhoushengfan@yahoo.com
基金资助:
国家自然科学基金(11871437);国家自然科学基金(11971356)

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

Zongfei Han,Shengfan Zhou*()

^{College of Mathematics and Computer Science, Zhejiang Normal University, Zhejiang Jinhua 321004}

Received:2019-03-29 Online:2020-06-26 Published:2020-07-15
Contact: Shengfan Zhou E-mail:zhoushengfan@yahoo.com
Supported by:
the NSFC(11871437);the NSFC(11971356)

摘要/Abstract

摘要：

该文考虑非自治随机FitzHugh-Nagumo系统的随机指数吸引子（具有有限分形维数且指数吸引轨道的正不变紧可测集）的存在性，这表明该系统解的长期行为可以用有限个独立参数刻画.证明的关键是系统的解的尾估计和分解系统的两解之差为三部分，其中一部分属于有限维空间，另外两部分在时间变量和空间变量充分大时都变得足够小.

关键词: 非自治随机FitzHugh-Nagumo系统, 随机指数吸引子, 乘法白噪声, 分形维数

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

中图分类号:

韩宗飞,周盛凡. 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[J]. 数学物理学报, 2020, 40(3): 756-783.

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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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

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

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