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.
引用
收藏
页码：1689 / 1720
页数：32
相关论文
共 50 条
  • [21] Singleton sets random attractor for stochastic FitzHugh-Nagumo lattice equations driven by fractional Brownian motions
    Gu, Anhui
    Li, Yangrong
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (11) : 3929 - 3937
  • [22] Dynamics of stochastic FitzHugh-Nagumo systems with additive noise on unbounded thin domains
    Shi, Lin
    Li, Dingshi
    Li, Xiliang
    Wang, Xiaohu
    STOCHASTICS AND DYNAMICS, 2020, 20 (03)
  • [23] LONG TERM BEHAVIOR OF RANDOM NAVIER-STOKES EQUATIONS DRIVEN BY COLORED NOISE
    Gu, Anhui
    Guo, Boling
    Wang, Bixiang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (07): : 2495 - 2532
  • [24] Asymptotic Behavior of Weakly Dissipative Fractional Wave Equations Driven by Superlinear Colored Noise on RN
    Wang, Renhai
    Chen, Pengyu
    Wang, Bixiang
    JOURNAL OF GEOMETRIC ANALYSIS, 2025, 35 (03)
  • [25] Continuity and random dynamics of the non-autonomous stochastic FitzHugh-Nagumo system on RN
    Zhao, Wenqiang
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (10) : 3801 - 3824
  • [26] ASYMPTOTIC BEHAVIOR OF SUPERCRITICAL WAVE EQUATIONS DRIVEN BY COLORED NOISE ON UNBOUNDED DOMAINS
    Wang, Bixiang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, : 4185 - 4229
  • [27] Stochastic dynamic behavior of FitzHugh-Nagumo neurons stimulated by white noise
    Li, Tao
    Wu, Kaijun
    Yan, Mingjun
    Liu, Zhengnan
    Zheng, Huan
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2021, 35 (10):
  • [28] Stochastic impact in Fitzhugh-Nagumo neural system with time delays driven by colored noises
    Li Sheng-Hong
    Zhu Quan-Xin
    CHINESE JOURNAL OF PHYSICS, 2018, 56 (01) : 346 - 354
  • [29] Random uniform attractors for fractional stochastic FitzHugh-Nagumo lattice systems
    Li, Xintao
    Gao, Yunlong
    AIMS MATHEMATICS, 2024, 9 (08): : 22251 - 22270
  • [30] Well-posedness and dynamics of fractional FitzHugh-Nagumo systems on Double-struck capital RNdriven by nonlinear noise
    Wang, Renhai
    Guo, Boling
    Wang, Bixiang
    SCIENCE CHINA-MATHEMATICS, 2021, 64 (11) : 2395 - 2436
12345