Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka–Volterra competition system with diffusion

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka–Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c⁎ such that for each wave speed c⩽c⁎, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed cc⁎.

RésuméOn étudie lʼexistence, lʼunicité, et la stabilité asymptotique des ondes progressives périodiques pour un système compétitif de Lotka–Volterra avec diffusion. Sous certaines conditions, on démontre quʼil existe une vitesse maximale c⁎ telle que pour chaque vitesse cc⁎.