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Journal of Applied Mathematics
Volume 2012, Article ID 969425, 18 pages
http://dx.doi.org/10.1155/2012/969425
Research Article

Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy

1School of Life and Environmental Science, Wenzhou University, Zhejiang, Wenzhou 325035, China
2School of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035, China
3Institute of Mathematics, Academia Sinica, Beijing 100080, China

Received 9 March 2012; Revised 1 May 2012; Accepted 1 May 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Min 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

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.