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)

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.