Theoretical and numerical analysis of solutions of some systems of nonlinear difference equations

In this paper, we obtain the form of the solutions of the following rational systems of difference equations

$$x_{n+1}={\displaystyle \frac{y_{n-1}{z}_n}{z_n\pm x_{n-2}}},y_{n+1}={\displaystyle \frac{z_{n-1}{x}_n}{x_n\pm y_{n-2}}},z_{n+1}={\displaystyle \frac{x_{n-1}{y}_n}{y_n\pm z_{n-2}}},$$

with initial values are non-zero real numbers.