Traveling wave solutions indelayed reaction diffusion systems with applications tomulti-species models

Abstract

This paper is concerned with the existence of traveling wavesolutions in delayed reaction diffusion systems which at leastcontain multi-species competition, cooperation and predator-preymodels with diffusion and delays. By introducing the mixedquasimonotone condition and the exponentially mixed quasimonotonecondition, we reduce the existence of traveling wave solutions tothe existence of a pair of admissible upper-lower solutions. Toillustrate our main results, the existence of traveling wavesolutions of multi-species competition, cooperation andpredator-prey Lotka-Volterra systems with delays is considered. Inparticular, we show the precisely asymptotic behavior of thetraveling wave solutions of these Lotka-Volterra systems.