Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 752403, 18 pages
Research Article

Extinction and Permanence of a Three-Species Lotka-Volterra System with Impulsive Control Strategies

Hunki Baek

Department of Mathematics, Kyungpook National University, Daegu 702701, South Korea

Received 8 June 2008; Accepted 8 September 2008

Academic Editor: Juan Jose Nieto

Copyright © 2008 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.


A three-species Lotka-Volterra system with impulsive control strategies containing the biological control (the constant impulse) and the chemical control (the proportional impulse) with the same period, but not simultaneously, is investigated. By applying the Floquet theory of impulsive differential equation and small amplitude perturbation techniques to the system, we find conditions for local and global stabilities of a lower-level prey and top-predator free periodic solution of the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. We also give a numerical example that seems to indicate the existence of chaotic behavior.