Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal

This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.