On a solvable rational system of difference equations

摘要

We show that the system of difference equationsxn+1=xnyn-kyn-k+1(an+bnxnyn-k),yn+1=ynxn-kxn-k+1(cn+dnynxn-k),n∈N0,where k∈N, the sequences an,bn,cn,dn, n∈N0, and initial values x-i,y-i,i=0,k¯ are real numbers can be solved in closed form. By using obtained formulae we investigate asymptotic behavior of well-defined solutions of the system for the case when all the sequences an, bn,cn and dn are constant.