Random attractors forstochastic   FitzHugh-Nagumo systemsdriven by  deterministic non-autonomous forcing

Abiti Adili; Bixiang Wang

doi:10.3934/dcdsb.2013.18.643

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2013, Volume 18, Issue 3: 643-666. Doi: 10.3934/dcdsb.2013.18.643

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Random attractors for stochastic FitzHugh-Nagumo systems driven by deterministic non-autonomous forcing

Abiti Adili^1, and
Bixiang Wang^1,

1.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Received: April 30, 2012

Revised: August 31, 2012

Published: April 2013

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Abstract

This paper is concerned with the asymptotic behavior of solutions of the FitzHugh-Nagumo system on $\mathbb{R}^n$ driven by additive noise and deterministic non-autonomous forcing. We prove the system has a random attractor which pullback attracts all tempered random sets. We also prove the periodicity of the random attractor when the system is perturbed by time periodic forcing. The pullback asymptotic compactness of solutions is established by uniform estimates on the tails of solutions outside a large ball in $\mathbb{R}^n$.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 37L30, 35R60, 60H15.

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