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2010, Volume 14, Issue 1: 159-176. Doi: 10.3934/dcdsb.2010.14.159
This issue Previous Article Existence of traveling wave solutions for a nonlocal reaction-diffusion model of influenza a drift Next Article Limit behavior of nonlinear stochastic wave equations with singular perturbation

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

  • 1.

    Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064

  • 2.

    Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064

Received:  August 2009
Revised:  November 2009
Published:  July 2010
Abstract / Introduction Related Papers Cited by
    Abstract
  • Recently a discrete-time prey-predator model with Holling type II was discussed for its bifurcations so as to show its complicated dynamical properties. Simulation illustrated the occurrence of invariant cycles. In this paper we first clarify the parametric conditions of non-hyperbolicity, correcting a known result. Then we apply the center manifold reduction and the method of normal forms to completely discuss bifurcations of codimension 1. We give bifurcation curves analytically for transcritical bifurcation, flip bifurcation and Neimark-Sacker bifurcation separately, showing bifurcation phenomena not indicated in the previous work for the system.
    Mathematics Subject Classification: 37G10, 39A05, 34C23, 92D30.

    Citation:
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