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

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  • 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 $\mathbb{R}^n$.
    Mathematics Subject Classification: Primary: 37L55; Secondary: 37L30, 35R60, 60H15.

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