Time Periodic Traveling Waves For A Periodic Bistable Lotka-Volterra Competition System

In this paper.we study the existence, uniqueness and asymptotic stability of time traveling wave solutions to a parabolic Lotka-Volterra competition system Under certain conditions, we prove that there exists a wave speed c such that there is a time periodic traveling wave solution connecting two semi-trivial periodic solutions of the corresponding kinetic system. Moreover, we show the uniqueness of traveling wave solution through the sliding method. The stability of traveling wave solution is established by comparison principle, suitably constructed super-and sub-solutions and the method of squeezing in Chapter4.