Traveling waves for a three-species competition system with two weak aboriginal competitors

Abstract

In this paper, we study the traveling wave solutions for a three species competition system with two weak aboriginal competitors and one strong alien competitor. We are concerned with the existence of traveling waves such that these two co-existence aboriginal competitors are wiped out by the invading alien strong competitor. First, we derive the existence of wave profiles based on an application of Schauder's fixed point theorem with the help of constructing suitable generalized upper-lower solutions to capture the unstable wave tail limit. Then a new method for deriving the stable wave tail limit is introduced. Finally, the minimal invading speed is characterized.