具有马尔可夫切换的随机结构动态系统在集中点下的稳定性

IF 1.8 3区 数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-05-19 DOI:10.3934/math.20231245
T. Lukashiv, I. Malyk, Maryna K. Chepeleva, P. Nazarov
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引用次数: 0

摘要

本文旨在研究具有随机结构的随机微分方程平凡解的稳定性的充分条件,特别是在涉及存在集中点的情况下。渐近稳定性的证明利用了李雅普诺夫函数的使用,辅以对跳跃幅度和跳跃时间的附加约束,以及系统解的马尔可夫性质。通过一个算例说明了系统的稳定和不稳定情况。这部作品的新颖之处在于考虑了跳跃集中点,这在经典作品中是没有考虑到的。集中点存在的假设导致了对跳跃、跳跃时间和它们之间关系的附加约束。
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Stability of stochastic dynamic systems of a random structure with Markov switching in the presence of concentration points
This article aims to investigate sufficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them.
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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