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Abstract and Applied Analysis
Volume 2014, Article ID 304568, 10 pages
http://dx.doi.org/10.1155/2014/304568
Research Article

The Dynamics of a Nonautonomous Predator-Prey Model with Infertility Control in the Prey

1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
2Department of Mathematics, Yuncheng University, Yuncheng 044000, China

Received 16 December 2013; Accepted 20 January 2014; Published 10 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Xiaomei Feng 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 nonautonomous predator-prey model with infertility control in the prey is formulated and investigated. Threshold conditions for the permanence and extinction of fertility prey and infertility prey are established. Some new threshold values of integral form are obtained. For the periodic cases, these threshold conditions act as sharp threshold values for the permanence and extinction of fertility prey and infertility prey. There are also mounting concerns that the quantity of biological sterile drug is obtained in the process of the prevention and control of pest in the grasslands and farmland. Finally, two examples are given to illustrate the main results of this paper. The numerical simulations shown that, when the pest population is permanet, different dynamic behaviors may be found in this model, such as the global attractivity and the chaotic attractor.