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Random attractors of FitzHugh–Nagumo systems driven by colored noise on unbounded domains

Anhui Gu

http://orcid.org/0000-0002-8713-6888

School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China

E-mail Address: gahui@swu.edu.cn

Corresponding author.

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and

Bixiang Wang

Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

E-mail Address: bwang@nmt.edu

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https://doi.org/10.1142/S0219493719500357Cited by:10 (Source: Crossref)

Abstract

We investigate the pathwise asymptotic behavior of the FitzHugh–Nagumo systems defined on unbounded domains driven by nonlinear colored noise. We prove the existence and uniqueness of tempered pullback random attractors of the systems with polynomial diffusion terms. The pullback asymptotic compactness of solutions is obtained by the uniform estimates on the tails of solutions outside a bounded domain. We also examine the limiting behavior of the FitzHugh–Nagumo systems driven by linear colored noise as the correlation time of the colored noise approaches zero. In this respect, we prove that the solutions and the pullback random attractors of the systems driven by linear colored noise converge to that of the corresponding stochastic systems driven by linear white noise.

Keywords:

AMSC: 35B40, 35B41, 37L30

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