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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 137182, 14 pages
http://dx.doi.org/10.1155/2015/137182
Research Article

Dynamics of Planar Systems That Model Stage-Structured Populations

Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA

Received 20 May 2015; Accepted 27 August 2015

Academic Editor: Aleksei A. Koronovskii

Copyright © 2015 N. Lazaryan and H. Sedaghat. 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 study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two oscillations.