Propagation dynamics of a three species predator-prey system with a pair of strong-weak competing predators

Abstract

We are concerned with propagation phenomenon of a three-species system involving a single prey and a pair of strong-weak competing predators. More accurately, we shall mainly consider situations when the simple prey is an indigenous species, and one of the two predators is aboriginal, while the other is alien. In any case, under certain parameters, three species can finally coexist. Naturally, we have obtained that when a weak competing predator is an aboriginal species, the strong predator can successfully invade the environment and become dominant species, leading to the extinction of its weak counterpart. Particularly, we can construct traveling wave solution where the weak predator invades the environment inhabited by its strong competitor and replaces aboriginal strong counterpart, which depends on higher biomass rate of the weak predator. At last, we get the minimal wave speeds for these traveling waves in these situations.