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

Global asymptotic stability in a class of difference equations

Xiaofan Yang1 , Limin Cui2 , Yuan Yan Tang1 and Jianqiu Cao4

1College of Computer Science, Chongqing University, Chongqing 400044, China
 2Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong
 4School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, China

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.