Abstract: “In this paper, to depict the ecological world realistically, we adopt a two preys and one predator system with hybrid types of functional response, Holling type and Beddington-DeAngelis type. In fact, we show that this system is dissipative and find a necessary condition for the existence of the predator species. In addition, conditions for the persistence of the system are found. And we give a numerical example to attest to our theoretical results. Furthermore, the existence of chaotic phenomena is illustrated by bifurcation diagrams of the system.”

Keywords: predator-prey system, Holling type, Beddington-DeAngelis type, dissipative system, persistence, bifurcation diagram.