Qualitative properties of traveling wavefronts for a three-component lattice dynamical system with delay

Abstract

This article concerns a three-component delayed lattice dynamical system arising in competition models. In such models, traveling wave solutions serve an important tool to understand the competition mechanism, i.e. which species will survive or die out eventually. We first prove the existence of the minimal wave speed of the traveling wavefronts connecting two equilibria (1,0,1) and (0,1,0). Then, for sufficiently small intra-specific competitive delays, we establish the asymptotic behavior of the traveling wave solutions at minus/plus infinity. Finally the strict monotonicity and uniqueness of all traveling wave solutions are obtained for the case where intra-specific competitive delays are zeros. In particular, the effect of the delays on the minimal wave speed and the decay rate of the traveling profiles at minus/plus infinity is also investigated.