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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 656920, 13 pages
http://dx.doi.org/10.1155/2013/656920
Research Article

Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey

Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China

Received 13 June 2013; Accepted 5 September 2013

Academic Editor: XianHua Tang

Copyright © 2013 Lianwen Wang and Zhijun Liu. 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 a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.