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