Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 406821, 17 pages
http://dx.doi.org/10.1155/2012/406821
Research Article

The Form of the Solutions and Periodicity of Some Systems of Difference Equations

M. Mansour,1,2 M. M. El-Dessoky,1,2 and E. M. Elsayed1,2

1Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 20 May 2012; Accepted 6 July 2012

Academic Editor: Garyfalos Papaschinopoulos

Copyright © 2012 M. Mansour 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

This paper is devoted to get the form of the solutions and the periodic nature of the following systems of rational difference equations 𝑥 𝑛 + 1 = 𝑥 𝑛 − 5 / ( − 1 + 𝑥 𝑛 − 5 𝑦 𝑛 − 2 ) , 𝑦 𝑛 + 1 = 𝑦 𝑛 − 5 / ( ± 1 ± 𝑦 𝑛 − 5 𝑥 𝑛 − 2 ) , where the initial conditions are real numbers.