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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 160672, 11 pages
http://dx.doi.org/10.1155/2015/160672
Research Article

Basin of Attraction through Invariant Curves and Dominant Functions

1Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Alkhoud, 123 Muscat, Oman
2Sciences and Engineering, Paris-Sorbonne University Abu Dhabi, P.O. Box 38044, Abu Dhabi, UAE

Received 9 February 2015; Accepted 6 May 2015

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 Ziyad AlSharawi 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

We study a second-order difference equation of the form , where both and are decreasing. We consider a set of invariant curves at and use it to characterize the behaviour of solutions when and when . The case is related to the Y2K problem. For , we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria.