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Journal of Applied Mathematics
Volume 2014, Article ID 186232, 7 pages
http://dx.doi.org/10.1155/2014/186232
Research Article

Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

1Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China
2Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China

Received 11 January 2014; Accepted 22 May 2014; Published 12 June 2014

Academic Editor: Sabri Arik

Copyright © 2014 Ronghua Tan et al. 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

This is a continuation of the work of Tan et al. (2012). In this paper a periodic single species model controlled by constant impulsive perturbation is investigated. The constant impulse is realized at fixed moments of time. With the help of the comparison theorem of impulsive differential equations and Lyapunov functions, sufficient conditions for the permanence and global attractivity are established, respectively. Also, by comparing the above results with corresponding known results of Tan et al. (2012) (i.e., the above model with linear impulsive perturbations), we find that the two different types of impulsive perturbations have influence on the above dynamics. Numerical simulations are presented to substantiate our analytical results.