Existence and stability of traveling wavefronts for a three‐species Lotka–Volterra competitive‐cooperative system with nonlocal dispersal

Abstract

The purpose of this work is to investigate the existence and stability of traveling wavefronts for a three‐species competitive‐cooperative system with nonlocal dispersal. By applying monotone iteration method combining with a pair of suitable super‐ and sub‐solutions, we establish the existence of traveling wavefronts. The nonexistence of traveling wavefronts is obtained by a contradiction argument. Finally, by using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with relatively large speeds are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wavefronts decays exponentially at negative infinity, but in other locations, the initial data can be very large.