On a system of difference equations which can be solved in closed form

Abstract

We present an elegant method for solving the system of difference equationsxn+1=1xn+αyn,yn+ 1=βxn+1yn,naεℕ0, where parameters α and β and the initial values x0 and y0 are positive numbers, and by using obtained formulae we show that every solution of the system converges to a two-periodic solution.