Synchronized stationary distribution of stochastic multi-group models with dispersal

This paper is concerned with a new stationary distribution named synchronized stationary distribution. It is the first time to apply such kind of distribution to stochastic multi-group models with dispersal. And the existing region of synchronized stationary distribution is closely related to the coupling structure, stochastic disturbance intensity as well as the coefficients of models. We propose two main theorems to ensure the existence of a synchronized stationary distribution by combining Kirchhoff’s Matrix Tree Theorem in the graph theory as well as the Lyapunov method. Additionally, the value of our results is shown by applying them to stochastic coupled oscillators and stochastic coupled Rössler-like circuits with multiple dispersal. Correspondingly, two numerical examples are given to illustrate that our results are feasible and effective.