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

Xintao Li; Lianbing She; Rongrui Lin; Xintao Li; Lianbing She; Rongrui Lin

doi:10.3934/math.2024918

AIMS Mathematics

2024, Volume 9, Issue 7: 18860-18896. doi: 10.3934/math.2024918

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

School of Mathematics and Statistics, Liupanshui Normal University, Liupanshui 553004, China

Received: 31 January 2024 Revised: 06 May 2024 Accepted: 21 May 2024 Published: 05 June 2024
MSC : 35B40, 35B41, 37L30

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.
- FitzHugh-Nagumo lattice systems,
- nonlinear noise,
- weighted space,
- invariant measures,
- delay
Citation: Xintao Li, Lianbing She, Rongrui Lin. Invariant measures for stochastic FitzHugh-Nagumo delay lattice systems with long-range interactions in weighted space[J]. AIMS Mathematics, 2024, 9(7): 18860-18896. doi: 10.3934/math.2024918

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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.

References

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