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 novel model of multi-group models with dispersal and stochastic perturbation, in which dispersal among groups and stochastic perturbation are considered at the same time. By combining graph theory with Lyapunov method, some sufficient criteria are derived to guarantee global exponential stability of the model. Furthermore, a criterion is successfully applied to stochastic coupled oscillator systems described by two digraphs. Finally, we offer a numerical example to illustrate the effectiveness of the main results.