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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5963594, 15 pages
https://doi.org/10.1155/2017/5963594
Research Article

Global Asymptotic Stability for Discrete Single Species Population Models

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Correspondence should be addressed to M. R. S. Kulenović; ude.iru.liam@civonelukm

Received 28 March 2017; Accepted 16 May 2017; Published 13 June 2017

Academic Editor: Rigoberto Medina

Copyright © 2017 A. Bilgin and M. R. S. Kulenović. 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 present some basic discrete models in populations dynamics of single species with several age classes. Starting with the basic Beverton-Holt model that describes the change of single species we discuss its basic properties such as a convergence of all solutions to the equilibrium, oscillation of solutions about the equilibrium solutions, Allee’s effect, and Jillson’s effect. We consider the effect of the constant and periodic immigration and emigration on the global properties of Beverton-Holt model. We also consider the effect of the periodic environment on the global properties of Beverton-Holt model.