Abstract and Applied Analysis
Volume 2009 (2009), Article ID 695121, 19 pages
Research Article

Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations

Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

Received 3 March 2009; Accepted 7 August 2009

Academic Editor: Stephen Clark

Copyright © 2009 Hunki Baek and Younghae Do. 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.


We study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.