Advances in Difference Equations
Volume 2007 (2007), Article ID 16249, 7 pages
doi:10.1155/2007/16249
Research Article

Global Asymptotic Stability in a Class of Difference Equations

Xiaofan Yang,1,2 Limin Cui,3 Yuan Yan Tang,1,3 and Jianqiu Cao2

1College of Computer Science, Chongqing University, Chongqing 400044, China
2School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, China
3Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong

Received 29 April 2007; Accepted 5 November 2007

Academic Editor: John R. Graef

Copyright © 2007 Xiaofan Yang 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 difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui}≤f(u1,…,ur)≤max1≤i≤r{ui,1/ui},(u1,…,ur)T∈(R+)r. We prove that this difference equation admits c=1 as the globally asymptotically stable equilibrium. This result extends and generalizes some previously known results.