The form of solutions and periodicity for some systems of third‐order rational difference equations

In this paper, we deal with the system that has solutions and the periodicity character of the following systems of rational difference equations with order threex n + 1 =y n − 1y n − 2x n± 1 ± y n − 1y n − 2,y n + 1 =x n − 1x n − 2y n± 1 ± x n − 1x n − 2,with initial conditions x −2 , x −1 , x 0 , y −2 , y −1 , and  y 0  that are arbitrary nonzero real numbers. Some numerical examples will be given to illustrate our results. Copyright © 2015 John Wiley & Sons, Ltd.