Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 752403, 18 pages
doi:10.1155/2008/752403
Research Article
Extinction and Permanence of a Three-Species Lotka-Volterra System with Impulsive Control Strategies
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.
Abstract
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.