Advances in Difference Equations
Volume 2010 (2010), Article ID 954684, 15 pages
doi:10.1155/2010/954684
Research Article

Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments

Jianjun Jiao1 and Lansun Chen2

1Guizhou Key Laboratory of Economic System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China
2Institute of Mathematics, Academy of Mathematics and System Sciences, Beijing 100080, China

Received 21 August 2010; Accepted 22 September 2010

Academic Editor: Kanishka Perera

Copyright © 2010 Jianjun Jiao and Lansun Chen. 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

We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the permanence of the investigated system is also obtained. Our results provide reliable tactic basis for the practical biological economics management.