Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 419789, 8 pages
http://dx.doi.org/10.1155/2011/419789
Research Article

On the Dynamics of a Higher-Order Rational Difference Equation

A. M. Ahmed

Department of Natural Sciences, Arriyadh Community College, King Saud University, Malaz, P.O. Box 28095, Riyadh 11437, Saudi Arabia

Received 23 May 2011; Revised 2 August 2011; Accepted 6 August 2011

Academic Editor: Cengiz Çinar

Copyright © 2011 A. M. Ahmed. 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

The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equation 𝑥 𝑛 + 1 = 𝛼 𝑥 𝑛 − 1 / ( 𝛽 + 𝛾 Π 𝑘 𝑖 = 𝑙 𝑥 𝑝 𝑖 𝑛 − 2 𝑖 ) , 𝑛 = 0 , 1 , 2 , … , where the parameters 𝛼 , 𝛽 , 𝛾 , 𝑝 𝑙 , 𝑝 𝑙 + 1 , … , 𝑝 𝑘 are nonnegative real numbers, and 𝑙 , 𝑘 are nonnegative integers such that 𝑙 ≤ 𝑘 .