Advances in Difference Equations
Volume 2010 (2010), Article ID 505906, 10 pages
doi:10.1155/2010/505906
Research Article

Asymptotic Behavior of Equilibrium Point for a Family of Rational Difference Equations

Chang-you Wang,1,2,3 Qi-hong Shi,4 and Shu Wang3

1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control and Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China
3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
4Fundamental Department, Hebei College of Finance, Baoding 071051, China

Received 7 August 2010; Accepted 19 October 2010

Academic Editor: Rigoberto Medina

Copyright © 2010 Chang-you Wang 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

This paper is concerned with the following nonlinear difference equation xn+1=∑i=1lAsixn-si/(B+C∏j=1kxn-tj)+Dxn,  n=0,1,…, where the initial data x-m,x-m+1,…,x-1,  x0∈ℝ+, m=max⁡{s1,…,sl,t1,…,tk}, s1,…,sl,t1,…,tk are nonnegative integers, and Asi, B, C, and D are arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium x̅=0 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the work of Çinar (2004), Yang et al. (2005), and Berenhaut et al. (2007). In addition, some numerical simulations are also shown to support our analytic results.