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Research Article | Open Access

Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
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Abstract

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.

Keywords

Wong-Zakai approximationlattice systemsrandom attractorwhite noiseupper semicontinuity
CLC number: 37L30, 37L55, 37L60

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7569-7594
DOI: 10.3934/math.2022425

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Cite this article:
Li X. 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. https://doi.org/10.3934/math.2022425

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Received: 04 November 2021
Revised: 18 January 2022
Accepted: 24 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)