Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 791610, 10 pages
doi:10.1155/2010/791610
Research Article

Asymptotic Stability for a Class of Nonlinear Difference Equations

Chang-you Wang,1,2,3 Shu Wang,3 Zhi-wei Wang,4 Fei Gong,2,5 and Rui-fang Wang2,5

1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control & 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
4School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
5College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 9 January 2010; Accepted 5 February 2010

Academic Editor: Guang Zhang

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

We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max⁡⁡{l,k,s,t} and α,a,b,c are positive constants. Moreover, some numerical simulations are given to illustrate our results.