On the Periodic Solutions of Some Systems of Difference Equations

Abstract

In this paper, we study the solution of the systems of difference equations \begin{equation*} x_{n+1}=\frac{1\pm (y_{n}+x_{n-1})}{y_{n-2}},\ \ \ y_{n+1}=\frac{1\pm (x_{n}+y_{n-1})}{x_{n-2}},\;\;n=0,1,..., \end{equation*}% {\Large \noindent }where the initial conditions $x_{-2},\ x_{-1},\ x_{0},$ $% y_{-2},\ y_{-1},\ y_{0}$ are arbitrary non zero real numbers.