Advances in Difference Equations
Volume 2006 (2006), Article ID 16949, 7 pages
doi:10.1155/ADE/2006/16949

On the system of rational difference equations xn+1=f(xn,yn−k),yn+1=f(yn,xn−k)

Taixiang Sun,1 Hongjian Xi,2 and Liang Hong1

1Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530004, China

Received 15 September 2005; Revised 27 October 2005; Accepted 13 November 2005

Copyright © 2006 Taixiang Sun 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 behavior of the positive solutions of the system of rational difference equations xn+1=f(xn,yn−k),yn+1=f(yn,xn−k), n=0,1,2,…, under appropriate assumptions, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0,y−k,y−k+1,…,y0∈(0,+∞). We give sufficient conditions under which every positive solution of this equation converges to a positive equilibrium. The main theorem in [1] is included in our result.