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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 101649, 7 pages
http://dx.doi.org/10.1155/2013/101649
Research Article

A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36 123, Al-Khod, Oman

Received 17 June 2013; Revised 3 September 2013; Accepted 16 September 2013

Academic Editor: Yanni Xiao

Copyright © 2013 Ziyad AlSharawi. 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 consider discrete models of the form , where is a nonnegative p-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the recruitment function , we give a compact invariant region and use Brouwer fixed point theorem to prove the existence of a p-periodic solution. Also, we prove the global attractivity of the p-periodic solution when . In particular, this study gives theoretical results attesting to the belief that stocking (whether it is constant or periodic) preserves the global attractivity of the periodic solution in contest competition models with short delay. Finally, as an illustrative example, we discuss Pielou's model with periodic stocking.