Advances in Difference Equations
Volume 2006 (2006), Article ID 27637, 7 pages
doi:10.1155/ADE/2006/27637

Global behavior of a higher-order rational difference equation

Abstract

We investigate in this paper the global behavior of the following difference equation: xn+1=(Pk(xn−i0,xn−i1,…,xn−i2k)+b)/(Qk(xn−i0,xn−i1,…,xn−i2k)+b), n=0,1,…, under appropriate assumptions, where b∈[0,∞), k≥1, i0,i1,…,i2k∈{0,1,…} with i0<i1<…<i2k, the initial conditions xi−2k,xi−2k+1,…,x0∈(0,∞). We prove that unique equilibrium x¯=1 of that equation is globally asymptotically stable.