Bifurcations of a three-species prey-predator system with scavenger

Abstract

In this paper, we explore the existence of fixed points, local dynamical characteristics at fixed points, the existence of bifurcation sets at fixed points, and bifurcations of a three-species discrete prey-predator system with the scavenger. More specifically, it is proved that for all parameters, the discrete system has trivial and boundary fixed points; two more boundary fixed points, and an interior fixed point under a certain model's parametric restriction(s). Further, by the theory of linear stability, we examined local dynamics at fixed points. In order to understand the dynamics of the understudied system thoroughly, we studied the occurrence of certain bifurcations at fixed points by the bifurcation theory. Finally, theoretical results are numerically verified.