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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 431671, 10 pages
http://dx.doi.org/10.1155/2014/431671
Research Article

Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure

1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China
2Department of Basic Courses, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 10 June 2013; Accepted 6 January 2014; Published 25 February 2014

Academic Editor: Keshlan S. Govinder

Copyright © 2014 Lingshu Wang and Guanghui Feng. 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.

Abstract

A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.