Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains

Abstract

The regularity of random attractors is considered for the nonautonomous fractional stochastic FitzHugh-Nagumo system. We prove that the system has a pullback random attractor that is compact in H^s({\mathrm{ℝ}}^n)\times L^{\mathrm{2}}({\mathrm{ℝ}}^n) and attracts all tempered random sets of L^s({\mathrm{ℝ}}^n)\times L^{\mathrm{2}}({\mathrm{ℝ}}^n) in the topology of H^s({\mathrm{ℝ}}^n)\times L^{\mathrm{2}}({\mathrm{ℝ}}^n) with s\in (\mathrm{0},\mathrm{1}). By the idea of positive and negative truncations, spectral decomposition in bounded domains, and tail estimates, we achieved the desired results.

Key words： Fractional stochastic FitzHugh-Nagumo system; random attractor; asymptotic compactness

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