Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 285934, 24 pages
doi:10.1155/2009/285934
Global stability for a delayed predator-prey system with stage structure for the predator
Xiao Zhang
, Rui Xu
and Qintao Gan
Institute of Applied Mathematics, Shijiazhaung Mechanical Engineering College, Shijiazhuang 050003, China
Abstract
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.