Random attractor and exponentially stability for the second order nonautonomous retarded lattice systems with multiplicative white noise

Abstract

In this paper, we first present some conditions for the existence of a random attractor of continuous non-autonomous random dynamical systems (cocycle) and locally coupled stochastic retarded lattice dynamical systems in a space of continuous functions from finite closed interval into a product space of finite weighted spaces of infinite sequences. Then we consider the existence, singleton and exponentially stability of the random attractor for the second order non-autonomous retarded lattice systems with multiplicative white noise.