Nonlinear stability of traveling wave fronts to the Lotka–Volterra competition system

Abstract In this paper, based on the weighted energy method, the conditions on the nonlinear stability of traveling wave fronts of Lotka–Volterra competition system with any noncritical speeds are studied. More accurately, by revising some technical details, we have proved that when the diffusion parameter satisfies for any speeds , where is the critical speed, the traveling wave fronts are exponential stability. While, for other cases, in order to obtain the same stability results, the values of speeds could be larger. Our conclusions expand the ranges of the speeds that traveling wave fronts are stable, which improves previous results.