ASYMPTOTIC BEHAVIOR OF RANDOM FITZHUGH-NAGUMO SYSTEMS DRIVEN BY COLORED NOISE

被引：80
|
作者：
Gu, Anhui [1 ]
Wang, Bixiang [2 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 04期
关键词：
Random attractor; colored noise; white noise; FitzHugh-Nagumo system; FRACTIONAL BROWNIAN-MOTION; RANDOM DYNAMICAL-SYSTEMS; STOCHASTIC DIFFERENTIAL-EQUATIONS; RANDOM ATTRACTORS; PULLBACK ATTRACTORS; EVOLUTION-EQUATIONS; UNBOUNDED-DOMAINS; APPROXIMATION; EXISTENCE; UNIQUENESS;
D O I：
10.3934/dcdsb.2018072
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the existence and uniqueness of random attractors for the FitzHugh-Nagumo system driven by colored noise with a non-linear diffusion term. We demonstrate that the colored noise is much easier to deal with than the white noise for studying the pathwise dynamics of stochastic systems. In addition, we show the attractors of the random FitzHugh-Nagumo system driven by a linear multiplicative colored noise converge to that of the corresponding stochastic system driven by a linear multiplicative white noise.
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页码：1689 / 1720
页数：32
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