Complicate Dynamics of a Discrete Predator-prey Model with Competition Between Predators

Abstract

We consider a discrete predator-prey model with competition between predators in this paper. By simplifying the corresponding continuous predator-prey model, and using the semidiscretization method to obtain a new discrete model, we discuss the existence and local stability of nonnegative fixed points of the new discrete model. What’s more important, by using the bifurcation theory, we derive the sufficient conditions for the occurrences of Neimark-Sacker bifurcation and the stability of closed orbit bifurcated. Finally, the numerical simulation are presented, which not only illustrate the existence of NeimarkSacker bifurcation but also reveal some new dynamic phenomena of this model.