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Regularity of pullback attractors and equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains (1412.1160v2)

Published 3 Dec 2014 in math.AP

Abstract: A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, it is showed that every generated random cocycle has a pullback attractor in $Ll(\mathbb{R}N)\times L2(\mathbb{R}N)$ with $l\in(2,p]$, and the family of obtained attractors is upper semi-continuous at any intensity of noise. Moreover, if some additional conditions are added, then the system possesses a unique equilibrium and is attracted by a single point.

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