Infinitely many Equilibria and Some Codimension One Bifurcations in a Subsystem of a Two-Preys One-Predator Dynamical System

In this paper we study a two dimensional dynamical system depending on four parameters. This is a subsystem of a three dimensional system of two-preys one-predator system. Our focus is in the dynamics of the system and bifurcations with respect to the variation on the mortality rate of the predator. Interesting co-dimension one bifurcation such as transcritical and Hopf bifurcation have been observed. Furthermore, the system exhibit the existence of infinitely many equilibria as the bifurcation parameter become zero.