Regularity of pullback attractors and random equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains

This paper is concerned with the stochastic Fitzhugh-Nagumo system with non-autonomous terms as well as Wiener type multiplicative noises. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, the existences and upper semi-continuity of pullback attractors are proved for the generated random cocycle in $L^l(\mathbb{R}^N)\times L^2(\mathbb{R}^N)$ for any $l\in(2,p]$. The asymptotic compactness of the first component of the system in $L^p(\mathbb{R}^N)$ is proved by a new asymptotic a priori estimate technique, by which the plus or minus sign of the nonlinearity at large values is not required. Moreover, the condition on the existence of the unique random fixed point is obtained, in which case the influence of physical parameters on the attractors is analysed.