Periodicity and solutions for some systems of nonlinear rational difference equations

In this paper, we investigated the periodic nature and the form of the solutions of nonlinear di?erence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers. 

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