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Abstract and Applied Analysis
Volume 2014, Article ID 963072, 18 pages
http://dx.doi.org/10.1155/2014/963072
Research Article

Geometric Analysis of an Integrated Pest Management Model Including Two State Impulses

School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 10 December 2013; Accepted 20 January 2014; Published 19 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Wencai Zhao 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

According to integrated pest management strategies, we construct and investigate the dynamics of a Holling-Tanner predator-prey system with state dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Applying the Dulacs criterion, the global stability of the positive equilibrium in the system without impulsive effect is discussed. By using impulsive differential equation geometry theory and the method of successor functions, we prove the existence of periodic solution of the system with state dependent impulsive effects. Furthermore, the stability conditions of periodic solutions are obtained. Some simulations are exerted to illustrate the feasibility of our main results.