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Regularity of pullback attractors and random equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains
Keywords:Random dynamical system; non-autonomous FitzHugh-Nagumo system; upper semi-continuity; pullback attractor; random equilibria
      This paper is concerned with stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a wiener multiplicative noise. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, it is proved the existences and semi-continuousness of pullback attractors 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 and minus of the nonlinearity at large values are not required. Moreover, if some additional conditions are added to the physical parameters, then the system possesses a unique random fixed point.