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

Abstract

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.

Keywords:

• Non-autonomous stochastic FitzHugh–Nagumo system
• random uniform attractor
• random cocycle attractor
• multiplicative noise.

2010 Mathematics Subject Classifications:

• 37L55
• 35B41
• 35B40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 11871437, 11971356].