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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 195247, 6 pages
http://dx.doi.org/10.1155/2015/195247
Research Article

Global Attractor of Solutions of a Rational System in the Plane

1Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
2Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA
3Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA

Received 22 March 2015; Revised 14 July 2015; Accepted 15 July 2015

Academic Editor: Antonia Vecchio

Copyright © 2015 Miron B. Bekker 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 consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured that every positive solution of this system converges to a finite limit. Here we confirm this conjecture, subject to an additional assumption.