Traveling wave solutions of Lotka-Volterra type two predators-one prey model

In this work, we consider a model with one basal resource and two species of predators feeding by the same resource. There are three non-trivial boundary equilibria. One is the saturated state E-K of the prey without any predator. Other two equilibria, E-1 and E-2, are the coexistence states of the prey with only one species of predators. Using a high-dimensional shooting method, the Wazewski' principle, we establish the conditions for the existence of traveling wave solutions from E-K to E-2 and from E-1 to E-2. These results show that the advantageous species v(2) always win in the competition and exclude species v(1) eventually. Finally, some numerical simulations are presented, and biological interpretations are given. Copyright (c) 2016 John Wiley & Sons, Ltd.