On the system xn+1=ynxn-k/(yn-k+1(an+bnynxn-k)), yn+1=xnyn-k/(xn-k+1(cn+dnxnyn-k))

摘要

It is shown that the system of difference equationsxn+1=ynxn-kyn-k+1(an+bnynxn-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.