脉冲随机神经场晶格模型的动力学行为

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2024-04-30 DOI:10.1142/s0219493724500126

Tianhao Zeng, Shaoyue Mi, Dingshi Li

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引用次数: 0

摘要

本文关注非线性噪声驱动的脉冲随机神经场晶格模型解的渐近行为。我们首先证明了脉冲随机系统的弱回拉平均随机吸引子的存在性和唯一性。然后，根据马尔可夫过程的性质，建立了脉冲随机系统的量纲演化系统的存在性。为此，我们采用了对解的尾部进行均匀估计的思想，以证明网格系统解的分布族的紧密性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dynamical behaviors of an impulsive stochastic neural field lattice model

This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.