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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 574541, 16 pages
http://dx.doi.org/10.1155/2013/574541
Research Article

Optimal Control Policies of Pests for Hybrid Dynamical Systems

1School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China
2Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, China

Received 12 May 2013; Accepted 29 July 2013

Academic Editor: Sanyi Tang

Copyright © 2013 Baolin Kang 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

We improve the traditional integrated pest management (IPM) control strategies and formulate three specific management strategies, which can be described by hybrid dynamical systems. These strategies can not only effectively control pests but also reduce the abuse of pesticides and protect the natural enemies. The aim of this work is to study how the factors, such as natural enemies optimum choice in the two kinds of different pests, timings of natural enemy releases, dosages and timings of insecticide applications, and instantaneous killing rates of pesticides on both pests and natural enemies, can affect the success of IPM control programmes. The results indicate that the pests outbreak period or frequency largely depends on the optimal selective feeding of the natural enemy between one of the pests and the control tactics. Ultimately, we obtain the only pest needs to be controlled below a certain threshold while not supervising pest .