Time-periodic traveling waves for a periodic Lotka–Volterra competition system with nonlocal dispersal

Abstract

This paper is concerned with the time-periodic traveling waves for a periodic Lotka–Volterra competition system with nonlocal dispersal. Under the strong competition assumption, we first prove the existence of periodic traveling fronts connecting two stable semi-trivial periodic solutions. Then we establish the monotonicity and global exponential stability of smooth periodic traveling fronts. Since the standard strong comparison theorem does not hold for the Lotka–Volterra competition system, the monotonicity and global exponential stability are proved by establishing some new strong comparison theorems and constructing some auxiliary monotone systems. The Liapunov stability of the periodic traveling fronts is also proved.