Publications
Sort:
Open Access Research Article Issue
Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise
AIMS Mathematics 2022, 7(5): 7569-7594
Published: 15 May 2022
Abstract PDF (296.7 KB) Collect
Downloads:1

In this article, we investigate the Wong-Zakai approximations of a class of second order non-autonomous stochastic lattice systems with additive white noise. We first prove the existence and uniqueness of tempered pullback random attractors for the original stochastic system and its Wong-Zakai approximation. Then, we establish the upper semicontinuity of these attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.

Open Access Research Article Issue
Invariant measures for stochastic FitzHugh-Nagumo delay lattice systems with long-range interactions in weighted space
AIMS Mathematics 2024, 9(7): 18860-18896
Published: 15 July 2024
Abstract PDF (337.7 KB) Collect
Downloads:1

The focus of this paper lies in exploring the limiting dynamics of stochastic FitzHugh-Nagumo delay lattice systems with long-range interactions and nonlinear noise in weighted space. To begin, we established the well-posedness of solutions to these stochastic delay lattice systems and subsequently proved the existence and uniqueness of invariant measures.

Total 2