On a solvable rational system of difference equations

Abstract

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.