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Journal of Applied Mathematics
Volume 2012, Article ID 381503, 25 pages
http://dx.doi.org/10.1155/2012/381503
Research Article

Multi-State Dependent Impulsive Control for Pest Management

College of Science, Shandong University of Science and Technology, Qingdao 266510, China

Received 17 April 2012; Accepted 6 June 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Huidong Cheng 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 the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results. Our results show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.