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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 248291, 16 pages
http://dx.doi.org/10.1155/2012/248291
Research Article

Qualitative Study of Solutions of Some Difference Equations

1Department of Mathematics, Rabigh College of Science and Art, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 14 February 2012; Accepted 15 March 2012

Academic Editor: Chaitan Gupta

Copyright © 2012 Hamdy El-Metwally and E. M. Elsayed. 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 obtain in this paper the solutions of the following recursive sequences 𝑥 𝑛 + 1 = 𝑥 𝑛 𝑥 𝑛 3 / 𝑥 𝑛 2 ( ± 1 ± 𝑥 𝑛 𝑥 𝑛 3 ) , 𝑛 = 0 , 1 , , where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative behavior of the solutions such as the boundedness, the global stability, and the periodicity character of the solutions in each case have been studied. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the obtained results.