Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 252437, 17 pages
Research Article

Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 8 March 2012; Revised 3 May 2012; Accepted 4 May 2012

Academic Editor: Xiaohua Ding

Copyright © 2012 Yakui Xue and Xiaoqing Wang. 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.


A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.