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Journal of Applied Mathematics
Volume 2013, Article ID 678762, 8 pages
http://dx.doi.org/10.1155/2013/678762
Research Article

Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input

1Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, China
2Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China

Received 18 December 2012; Revised 3 August 2013; Accepted 23 August 2013

Academic Editor: Maoan Han

Copyright © 2013 Bing 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

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.