On the system of difference equations xn = xn - 1yn - 2ayn - 2 + byn - 1, yn = yn - 1xn - 2cxn - 2 + dxn - 1

Abstract

We show that the following system of difference equations xn=xn-1yn-2ayn-2+byn-1,yn=yn-1xn-2cxn-2+dxn-1,n∈N0, where parameters a, b, c, d, as well as initial values x-2,x-1,y-2,y-1, are real numbers, is solvable in closed form and by using obtained formulas we give some results on the long term behavior of their solutions. We also give natural explanations and considerably extend some recent results in the literature.