Well-posedness and dynamics of stochastic retarded FitzHugh-Nagumo lattice systems

This paper is concerned with the well-posedness as well as the time-dependent property of pullback random attractors for stochastic FitzHugh-Nagumo lattice systems with non-autonomous forcing terms, constant delay and multiplicative noise. First, we establish the well-posedness of such systems, which ensures the existence of a continuous non-autonomous random dynamical system. Next, the existence, uniqueness, forward compactness and long-time stability of pullback random attractors are proved. Eventually, we establish their upper semicontinuity as the time parameter tends to positive infinity and the delay time approaches zero, respectively.