Graph-Theoretical Method to the Existence of Stationary Distribution of Stochastic Coupled Systems |
| |
Authors: | Yan Liu Wenxue Li Jiqiang Feng |
| |
Institution: | 1.Department of Mathematics,Harbin Institute of Technology (Weihai),Weihai,People’s Republic of China;2.College of mathematics and statistics,Shenzhen University,Shenzhen,People’s Republic of China |
| |
Abstract: | In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|