The form of solutions and periodic nature for some rational difference equations systems

In this paper, we investigate the expressions of solutions and the periodic nature of the following systems of rational difference equations with order four xn+1=yn−3/±1±ynzn−1xn−2yn−3,yn+1=zn−3/±1±znxn−1yn−2zn−3,zn+1=xn−3/±1±xnyn−1zn−2xn−3, with initial conditions x − 3 ; x − 2 ; x − 1 ; x 0 ; y − 3 ; y − 2 ; y − 1 ; y 0 ; z − 3 ; z − 2 ; z − 1 and z 0 which are arbitrary real numbers.