Periodicity and solutions for some systems of nonlinear rational difference equations

Abstract

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.