Abstract
This paper is concerned with a time periodic Lotka-Volterra diffusion system with strong competition. We study the long time behavior of bounded solutions for the system that lie between two stable semi-trivial periodic solutions of the corresponding kinetic system. By transforming the competitive system into an equivalent cooperative system on [0,1], we first demonstrate local stability of a pair of diverging periodic traveling fronts. Then, by establishing a new Liouville-type theorem for solutions of the wave profile system and applying the truncation method, we prove asymptotic stability of these diverging periodic traveling fronts in the L∞-norm. Based on this result, by investigating the behavior of solutions with a one-parameter family of initial data, we present the trichotomy of parameter-dependent solutions: propagation for large parameter values, extinction for small parameter values, and transition from propagation to extinction for intermediate parameter values. Finally, we explore some properties of the threshold solution.