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Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 31614, 10 pages

Global attractivity of positive periodic solutions for an impulsive delay periodic “food limited” population model

College of Network Education, Lanzhou University of Technology, Lanzhou 730050, Gansu, China

Received 14 February 2006; Accepted 16 May 2006

Copyright © 2006 Jian Song. 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 will consider the following nonlinear impulsive delay differential equation N(t)=r(t)N(t)((K(t)N(tmw))/(K(t)+λ(t)N(tmw))), a.e. t>0, ttk, N(tk+)=(1+bk)N(tk), K=1,2,, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution N*(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of N*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.