Synchronized stationary distribution of stochastic coupled systems based on graph theory

摘要

This paper deals with the synchronized stationary distribution of stochastic coupled systems. The response system is constructed to help achieve a synchronized stationary distribution. Firstly, an error system obtained by the drive system and the response system is given and an appropriate Lyapunov function for the error system is constructed. On the basis of the graph theory and the Lyapunov method, some sufficient conditions are proposed to guarantee the existence of a stationary distribution for the error system, which reflects the coupling structure has a close relationship with synchronized stationary distribution. Then, an application to stochastic coupled oscillators is presented and sufficient conditions are obtained to illustrate the feasibility of the theoretical results. Finally, a numerical example is provided to demonstrate the effectiveness of theoretical results.