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 EK of the prey without any predator. Other two equilibria, E1 and E2, 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 EK to E2 and from E1 to E2. These results show that the advantageous species v2 always win in the competition and exclude species v1 eventually. Finally, some numerical simulations are presented, and biological interpretations are given.
Mathematical Methods in the Applied Sciences 39(18), p.5395–5408