Global exponential stability of multi-group models with multiple dispersal and stochastic perturbation based on graph-theoretic approach

Abstract

This paper is concerned with a more general model of multi-group models with multiple dispersal and stochastic perturbation, in which dispersal among multiple groups and stochastic perturbation are considered at the same time. By combining graph theory with Lyapunov method, we derive two types of sufficient criteria which are in the form of Lyapunov-type and coefficient-type respectively, to guarantee the global exponential stability of the model. Furthermore, coefficient-type criterion is successfully applied to stochastic coupled oscillators system. Finally, we offer a numerical example to illustrate the effectiveness and feasibility of the main results.