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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 519598, 8 pages
http://dx.doi.org/10.1155/2015/519598
Research Article

Periodic and Chaotic Orbits of a Discrete Rational System

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

Received 29 August 2014; Revised 9 January 2015; Accepted 15 January 2015

Academic Editor: Cengiz Çinar

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 rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane.