Bifurcations of a discrete prey-predator model with Holling type IIfunctional response

Abstract

Recently a discrete-time prey-predator model with Holling type IIwas discussed for its bifurcations so as to show its complicateddynamical properties. Simulation illustrated the occurrence ofinvariant cycles. In this paper we first clarify the parametricconditions of non-hyperbolicity, correcting a known result. Thenwe apply the center manifold reduction and the method of normalforms to completely discuss bifurcations of codimension 1. We givebifurcation curves analytically for transcritical bifurcation,flip bifurcation and Neimark-Sacker bifurcation separately,showing bifurcation phenomena not indicated in the previous workfor the system.