Random uniform attractor and random cocycle attractor for non-autonomous stochastic FitzHugh–Nagumo system on unbounded domains.

In this paper, we introduce the concept of uniform pullback asymptotic compactness of a non-autonomous random dynamical system, and prove the existence of random uniform and cocycle attractor with autonomous attraction universes for non-autonomous stochastic FitzHugh–Nagumo system with multiplicative noise defined on whole space. Some properties of random uniform and cocycle attractor are shown. The method of tail estimates plays an important role. [ABSTRACT FROM AUTHOR]