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Research Article | Open Access

Invariant measures for stochastic FitzHugh-Nagumo delay lattice systems with long-range interactions in weighted space

Xintao Li( ), Lianbing She, Rongrui Lin
School of Mathematics and Statistics, Liupanshui Normal University, Liupanshui 553004, China
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Abstract

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.

Keywords

FitzHugh-Nagumo lattice systemsnonlinear noiseweighted spaceinvariant measuresdelay
CLC number: 35B40, 35B41, 37L30

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 18860-18896
DOI: 10.3934/math.2024918

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Cite this article:
Li X, She L, Lin R. Invariant measures for stochastic FitzHugh-Nagumo delay lattice systems with long-range interactions in weighted space. AIMS Mathematics, 2024, 9(7): 18860-18896. https://doi.org/10.3934/math.2024918

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Received: 31 January 2024
Revised: 06 May 2024
Accepted: 21 May 2024
Published: 15 July 2024
©2024 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)