Periodic measures for a neural field lattice model with state dependent superlinear noise

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

doi:10.3934/era.2024180

Electronic Research Archive

2024, Volume 32, Issue 6: 4011-4024. doi: 10.3934/era.2024180

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Research article

Periodic measures for a neural field lattice model with state dependent superlinear noise

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

Received: 17 February 2024 Revised: 31 May 2024 Accepted: 04 June 2024 Published: 20 June 2024

The primary focus of this paper lies in exploring the limiting dynamics of a neural field lattice model with state dependent superlinear noise. First, we established the well-posedness of solutions to these stochastic systems and subsequently proved the existence of periodic measures for the system in the space of square-summable sequences using Krylov-Bogolyubov's method. The cutoff techniques of uniform estimates on tails of solutions was employed to establish the tightness of a family of probability distributions for the system's solutions.
- neural field lattice model,
- superlinear noise,
- periodic measure
Citation: Xintao Li, Rongrui Lin, Lianbing She. Periodic measures for a neural field lattice model with state dependent superlinear noise[J]. Electronic Research Archive, 2024, 32(6): 4011-4024. doi: 10.3934/era.2024180

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Abstract

The primary focus of this paper lies in exploring the limiting dynamics of a neural field lattice model with state dependent superlinear noise. First, we established the well-posedness of solutions to these stochastic systems and subsequently proved the existence of periodic measures for the system in the space of square-summable sequences using Krylov-Bogolyubov's method. The cutoff techniques of uniform estimates on tails of solutions was employed to establish the tightness of a family of probability distributions for the system's solutions.

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