Stability of multi-group models with cross-dispersal based on graph theory

We study the stability of multi-group models. We introduce cross-dispersal term when modeling and get a general multi-group model with cross-dispersal. Based on graph theory and Lyapunov functions method, some sufficient criteria are given, which contain Lyapunov-type theorem and coefficient-type theorem. Furthermore, in order to show the applicability of our results, an example about coupled oscillators with cross-dispersal is presented, and a coefficient-type criterion is provided to analyze the stability of it. Subsequently, a numerical simulation is given to demonstrate the validity and feasibility of the theoretic results.