Hopf Bifurcation of a Rosenzweig-Macarthur Hyperbolic Tangent-Type Predator-Prey Model

Abstract

In this paper, the Rosenzweig-MacArthur predator-prey model with the hyperbolic tangent functional response is investigated. We choose capturing efficiency of predator as the bifurcation parameter and mainly discuss the existence, direction and stability of Hopf bifurcation by Poincaré-Andronov-Hopf bifurcation theorem.