On a second order rational systems of difference equations

Abstract

In this paper we study the periodicity and the form of the solutions of the following systems of difference equations of order two xn+1 = \frac{y_{n}x_{n-1}}{\pm x_{n-1}\pm y_{n}}, yn+1 = \frac{x_{n}y_{n-1}}{\pm x_{n}\pm y_{n-1}}, n ∈ ℕ0, with nonzero real numbers initial conditions.