Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 982309, 17 pages
http://dx.doi.org/10.1155/2011/982309
Review Article

Solution and Attractivity for a Rational Recursive Sequence

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 15 February 2011; Accepted 26 March 2011

Academic Editor: Ibrahim Yalcinkaya

Copyright © 2011 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

This paper is concerned with the behavior of solution of the nonlinear difference equation 𝑥 𝑛 + 1 = 𝑎 𝑥 𝑛 − 1 + 𝑏 𝑥 𝑛 𝑥 𝑛 − 1 / ( 𝑐 𝑥 𝑛 + 𝑑 𝑥 𝑛 − 2 ) , 𝑛 = 0 , 1 , … , where the initial conditions 𝑥 − 2 , 𝑥 − 1 , 𝑥 0 are arbitrary positive real numbers and 𝑎 , 𝑏 , 𝑐 , 𝑑 are positive constants. Also, we give specific form of the solution of four special cases of this equation.