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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 285934, 24 pages
Research Article

Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator

Institute of Applied Mathematics, Shijiazhaung Mechanical Engineering College, Shijiazhuang 050003, China

Received 26 March 2009; Accepted 20 July 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Xiao Zhang et al. 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 delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.