Abstract and Applied Analysis
Volume 2010 (2010), Article ID 152378, 17 pages
doi:10.1155/2010/152378
Research Article

Long-Term Behavior of Solutions of the Difference Equation 𝑥 𝑛 + 1 = 𝑥 𝑛 − 1 𝑥 𝑛 − 2 − 1

Candace M. Kent,1 Witold Kosmala,2 and Stevo Stević3

1Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA
2Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608, USA
3Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 2 August 2010; Revised 24 October 2010; Accepted 28 October 2010

Academic Editor: Paul Eloe

Copyright © 2010 Candace M. Kent 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 investigate the long-term behavior of solutions of the following difference equation: 𝑥 𝑛 + 1 = 𝑥 𝑛 − 1 𝑥 𝑛 − 2 − 1 , 𝑛 ∈ ℕ 0 , where the initial values 𝑥 − 2 , 𝑥 − 1 , and 𝑥 0 are real numbers. Numerous fascinating properties of the solutions of the equation are presented.