On the system xn+1 = ynxn-k / (y n-k+1 (an + bn yn xn-k)), yn+1 = xnyn-k / (xn-k+1 (c n + dn xn yn-k))

Abstract

It is shown that the system of difference equationsxn+1=y nx n-kyn-k+1(an+bny nx n-k),yn+1=xnyn- kxn-k+1(cn+dnxnyn- k),n∈N0,where k∈N, the sequences an,bn,cn,dn, n∈N0, and the initial values x-i,y-i, i=0,k are real numbers can be solved in closed form. Asymptotic behavior of well-defined solutions of the system for the case when all the sequences an,bn, cn and dn are constant is studied in detail.