Abstract and Applied Analysis
Volume 2013 (2013), Article ID 179423, 10 pages
http://dx.doi.org/10.1155/2013/179423
Research Article

On the Period-Two Cycles of

S. Atawna,1 R. Abu-Saris,2 I. Hashim,1 and E. S. Ismail1

1School of Mathematical Sciences, The National of University of Malaysia, 43600 Bangi, Selangor, Malaysia
2Department of Basic Sciences, King Saud bin Abdulaziz University for Health Sciences, Riyadh 11426, Saudi Arabia

Received 2 January 2013; Revised 13 April 2013; Accepted 13 April 2013

Academic Editor: Douglas Anderson

Copyright © 2013 S. Atawna 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 consider the higher order nonlinear rational difference equation , where the parameters are positive real numbers and the initial conditions are nonnegative real numbers, . We give a necessary and sufficient condition for the equation to have a prime period-two solution. We show that the period-two solution of the equation is locally asymptotically stable.