Advances in Difference Equations
Volume 2006 (2006), Article ID 27637, 7 pages

Global behavior of a higher-order rational difference equation

Hongjian Xi and Taixiang Sun

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

Received 17 January 2006; Revised 6 April 2006; Accepted 12 April 2006

Copyright © 2006 Hongjian Xi and Taixiang Sun. 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.


We investigate in this paper the global behavior of the following difference equation: xn+1=(Pk(xni0,xni1,,xni2k)+b)/(Qk(xni0,xni1,,xni2k)+b), n=0,1,, under appropriate assumptions, where b[0,), k1, i0,i1,,i2k{0,1,} with i0<i1<<i2k, the initial conditions xi2k,xi2k+1,,x0(0,). We prove that unique equilibrium x¯=1 of that equation is globally asymptotically stable.