Traveling wave solutions for a predator–prey system with two predators and one prey

Abstract We study a predator–prey model with two alien predators and one aborigine prey in which the net growth rates of both predators are negative. We characterize the invading speed of these two predators by the minimal wave speed of traveling wave solutions connecting the predator-free state to the co-existence state. The proof of the existence of traveling waves is based on a standard method by constructing (generalized) upper-lower-solutions with the help of Schauder’s fixed point theorem. However, in this three species model, we are able to construct some suitable pairs of upper-lower-solutions not only for the super-critical speeds but also for the critical speed. Moreover, a new form of shrinking rectangles is introduced to derive the right-hand tail limit of wave profile.