Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

TL;DR

This paper establishes criteria for the existence of pullback attractors in stochastic lattice dynamical systems with non-autonomous deterministic and stochastic forcing, extending previous results to more general non-autonomous cases.

Contribution

It provides a new sufficient condition for the existence of pullback attractors in non-autonomous stochastic lattice systems with both deterministic and random forcing.

Findings

Proved existence of pullback attractors under new conditions.

Extended existing theories to non-autonomous stochastic systems.

Unified deterministic and stochastic forcing in attractor analysis.

Abstract

We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both deterministic non-autonomous forcing terms and multiplicative white noise. Our results recover many existing ones on the existences of pullback attractors for lattice dynamical systems with autonomous terms or white noises.