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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 767526, 10 pages
http://dx.doi.org/10.1155/2013/767526
Research Article

Periodicity and Permanence of a Discrete Impulsive Lotka-Volterra Predator-Prey Model Concerning Integrated Pest Management

Chang Tan1,2 and Jun Cao3

1College of Science, Northeast Forestry University, Harbin 150040, China
2Forestry Engineering Mobile Station, Northeast Forestry University, Harbin 150040, China
3College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China

Received 18 September 2013; Revised 23 November 2013; Accepted 25 November 2013

Academic Editor: Stefan Balint

Copyright © 2013 Chang Tan and Jun Cao. 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

By piecewise Euler method, a discrete Lotka-Volterra predator-prey model with impulsive effect at fixed moment is proposed and investigated. By using Floquets theorem, we show that a globally asymptotically stable pest-eradication periodic solution exists when the impulsive period is less than some critical value. Further, we prove that the discrete system is permanence if the impulsive period is larger than some critical value. Finally, some numerical experiments are given.