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Mathematical Problems in Engineering
Volume 2013, Article ID 329592, 11 pages
http://dx.doi.org/10.1155/2013/329592
Research Article

Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

1Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110819, China
2State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang, Liaoning 110819, China
3Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong

Received 7 February 2013; Accepted 11 April 2013

Academic Editor: Ligang Wu

Copyright © 2013 Chao Liu 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.

Abstract

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.