Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 892571, 12 pages
http://dx.doi.org/10.1155/2012/892571
Research Article

On the Solutions of a General System of Difference Equations

E. M. Elsayed,1,2 M. M. El-Dessoky,1,2 and Abdullah Alotaibi1

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 4 December 2011; Revised 14 February 2012; Accepted 16 February 2012

Academic Editor: Elena Braverman

Copyright © 2012 E. M. Elsayed 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 deal with the solutions of the systems of the difference equations 𝑥 𝑛 + 1 = 1 / 𝑥 𝑛 − 𝑝 𝑦 𝑛 − 𝑝 , 𝑦 𝑛 + 1 = 𝑥 𝑛 − 𝑝 𝑦 𝑛 − 𝑝 / 𝑥 𝑛 − 𝑞 𝑦 𝑛 − 𝑞 , and 𝑥 𝑛 + 1 = 1 / 𝑥 𝑛 − 𝑝 𝑦 𝑛 − 𝑝 𝑧 𝑛 − 𝑝 , 𝑦 𝑛 + 1 = 𝑥 𝑛 − 𝑝 𝑦 𝑛 − 𝑝 𝑧 𝑛 − 𝑝 / 𝑥 𝑛 − 𝑞 𝑦 𝑛 − 𝑞 𝑧 𝑛 − 𝑞 , 𝑧 𝑛 + 1 = 𝑥 𝑛 − 𝑞 𝑦 𝑛 − 𝑞 𝑧 𝑛 − 𝑞 / 𝑥 𝑛 − 𝑟 𝑦 𝑛 − 𝑟 𝑧 𝑛 − 𝑟 , with a nonzero real numbers initial conditions. Also, the periodicity of the general system of 𝑘 variables will be considered.