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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 935923, 15 pages
http://dx.doi.org/10.1155/2014/935923
Research Article

Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics

1Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Enshi, Hubei 445000, China
2Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, China
3Department of Mathematics and Information Sciences, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China

Received 21 November 2013; Revised 16 January 2014; Accepted 18 January 2014; Published 7 April 2014

Academic Editor: Yanni Xiao

Copyright © 2014 Mei Yan 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

Normally, chemical pesticides kill not only pests but also their natural enemies. In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. The effects of key parameters including killing efficiency rate, pulse period, the maximum birth effort per unit of time of natural enemy, and maturation time of prey on the threshold values are discussed in more detail. By comparing the two threshold values of mature prey-extinction, we provide the fact that the second control tactic is more effective than the first control method.