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Abstract and Applied Analysis
Volume 2013, Article ID 168340, 13 pages
Research Article

The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge

School of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China

Received 12 April 2013; Accepted 6 June 2013

Academic Editor: Luca Guerrini

Copyright © 2013 Shaoli Wang and Zhihao Ge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.