随机多组模型的平稳分布
Stationary Distribution Analysis for Stochastic Multi-Group Models

作者: 袁俊叶 , 张一帆 , 郭 英 :青岛理工大学理学院,山东 青岛;

关键词: 平稳分布图论随机多组模型随机耦合振子Stationary Distribution Graph Theory Stochastic Multi-Group Models Stochastic Coupled Oscillators

摘要:
本文主要利用图论的方法分析具有扩散的随机多组模型的平稳分布。然后,我们利用Lyapunov方法和图论得到了两^保证平稳分布存在的主要定理,其中得到的充分条件具有较少的保守性,反映了平稳分布与随机扰动和拓扑结构密切相关。此外,理论结果被应用到随机耦合振子中。最后, 通过数值模拟说明了本文结果的有效性。

Abstract: This paper mainly uses graph theory to analyze the stationary distribution for stochas- tic multi-group models with dispersal. Two main theorems are obtained to guarantee the existence of a stationary distribution via Lyapunov method and graph theory, in which sufficient conditions derived are less conservative and they reflect that station- ary distribution having a close connection with stochastic disturbance and topological structure. Furthermore, theoretical results are used to analyze tochastic coupled os- cillators. In the end, numerical simulation is given to demonstrate the availability of our results.

文章引用: 袁俊叶 , 张一帆 , 郭 英 (2021) 随机多组模型的平稳分布。 应用数学进展, 10, 1-15. doi: 10.12677/AAM.2021.101001

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