Stability and Bifurcation Analysis for a Predator-Prey Model with Crowley-Martin Functional Response

Abstract

This paper mainly focuses on the Gauze-type predator-prey model with Crowley-Martin functional response. The local stability of the equilibria is investigated by analyzing the characteristic equation and using the Routh-Hurwitz criterion. Besides, dynamic behavior has been studied by using the center manifold theorem and normal form theory. Finally, several numerical simulations not only verify the theoretical results of Hopf bifurcation but also display more interesting dynamical properties of the model.