Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 598495, 17 pages
doi:10.1155/2010/598495
Research Article

Dynamics of a Predator-Prey System Concerning Biological and Chemical Controls

Hye Kyung Kim1 and Hunki Baek2

1Department of Mathematics Education, Catholic University of Daegu, Kyongsan 712-702, Republic of Korea
2Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 25 August 2010; Accepted 13 November 2010

Academic Editor: Mohamed A. El-Gebeily

Copyright © 2010 Hye Kyung Kim and Hunki Baek. 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 investigate an impulsive predator-prey system with Monod-Haldane type functional response and control strategies, especially, biological and chemical controls. Conditions for the stability of the prey-free positive periodic solution and for the permanence of the system are established via the Floquet theory and comparison theorem. Numerical examples are also illustrated to substantiate mathematical results and to show that the system could give birth to various kinds of dynamical behaviors including periodic doubling, and chaotic attractor. Finally, in discussion section, we consider the dynamic behaviors of the system when the growth rate of the prey varies according to seasonal effects.