MONOTONE TRAVELING WAVES FOR DELAYED LOTKA-VOLTERRA COMPETITION SYSTEMS

We consider a delayed reaction-diffusion Lotka-Volterra competition system which does not generate a monotone semiflow with respect to the standard ordering relation for competitive systems. We obtain a necessary and sufficient condition for the existence of traveling wave solutions connecting the extinction state to the coexistence state, and prove that such solutions are monotone and unique (up to translation).