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

This paper is concerned with the asymptotic behavior ofsolutions of theFitzHugh-Nagumo system on $\mathbb{R}^n$ driven by additive noise anddeterministic non-autonomous forcing.We prove the system has a random attractor which pullback attractsall tempered random sets. We also prove the periodicity of therandom attractor when the system is perturbed by time periodic forcing.The pullback asymptotic compactness of solutions isestablished by uniform estimates on the tails of solutions outside a large ballin $\mathbb{R}^n$.