Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 827235, 12 pages
http://dx.doi.org/10.1155/2011/827235
Research Article

Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers

Li He1 and Wanping Liu2

1College of Computer Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2College of Computer Science, Chongqing University, Chongqing 400044, China

Received 19 June 2011; Accepted 17 July 2011

Academic Editor: Ibrahim Yalcinkaya

Copyright © 2011 Li He and Wanping Liu. 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

This paper studies a third-order conditional difference equation which is a generalization from the literature. We investigate this equation by transforming it into a first-order system. Finally it is proved that the equation has no period-two (or three) integer solutions. Besides, its all period-four (and five) integer solutions are derived under appropriate rational parameters.