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Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative noise

Pages: 1 - 10, Issue special, November 2013

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Abiti Adili - Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, United States (email)
Bixiang Wang - Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, United States (email)

Abstract: In this paper, we prove the existence and uniqueness of random attractors for the FitzHugh-Nagumo system defined on $\mathbb{R}^n$ driven by both deterministic non-autonomous forcing and multiplicative noise. The periodicity of random attractors is established when the system is perturbed by time periodic forcing. We also prove the upper semicontinuity of random attractors when the intensity of noise approaches zero.

Keywords:  Random attractor, periodic attractor, upper semicontinuity, unbounded domain, FitzHugh-Nagumo system.
Mathematics Subject Classification:  Primary: 37L55; Secondary: 37L30, 35R60, 60H15.

Received: September 2012;      Revised: December 2012;      Published: November 2013.

 References