Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 418564, 16 pages
http://dx.doi.org/10.1155/2012/418564
Research Article

Impulsive Perturbations of a Three-Species Food Chain System with the Beddington-DeAngelis Functional Response

Younghae Do,1 Hunki Baek,2 and Dongseok Kim3

1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
2Department of Mathematics Education, Catholic University of Daegu, Gyeongsan 712-702, Republic of Korea
3Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea

Received 26 July 2011; Accepted 2 October 2011

Academic Editor: Elena Braverman

Copyright © 2012 Younghae Do 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 dynamics of an impulsively controlled three-species food chain system with the Beddington-DeAngelis functional response are investigated using the Floquet theory and a comparison method. In the system, three species are prey, mid-predator, and top-predator. Under an integrated control strategy in sense of biological and chemical controls, the condition for extinction of the prey and the mid-predator is investigated. In addition, the condition for extinction of only the mid-predator is examined. We provide numerical simulations to substantiate the theoretical results.