随机多组模型的平稳分布  

Stationary Distribution Analysis for Stochastic Multi-Group Models

作　　者：农俊叶 张一帆 郭英 

机构地区：[1]青岛理工大学理学院,山东 青岛

出　　处：《应用数学进展》2021年第1期1-15,共15页Advances in Applied Mathematics

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。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.

关 键 词：平稳分布 图论 随机多组模型 随机耦合振子 

分 类 号：O15[理学—数学]