Stationary distribution of stochastic multi-group models with dispersal and telegraph noise

Graph-theoretic approach as a new technique is applied to analyze the issue of stationary distribution for stochastic multi-group models (MGMs) with Markovian switching and dispersal. The feature of our model is combining the white noise, the dispersal with Markovian switching, which can model systems in practice reasonably. By constructing a global Lyapunov function for stochastic MGMs with Markovian switching and dispersal, sufficient criteria, which guarantee the existence of a stationary distribution, are presented via the combination of the graph theory, the Lyapunov method and the M-matrix method. Moreover, stochastic coupled oscillators with Markovian switching and dispersal are presented as a practical application to illustrate our results in the end.