  The aim of this paper is to investigate the dynamics of a higher order system
of rational difference equations. Our concentration is on boundedness
character, the oscillatory, the existence of unbounded solutions and the global
behavior of positive solutions for the following system of difference equations
\begin{equation*} x_{n+1}=A+\frac{x_{n-m}}{z_{n}},\
y_{n+1}=A+\frac{y_{n-m}}{z_{n}},\ z_{n+1}=A+\frac{z_{n-m}}{y_{n}},\
n=0,1,...,\end{equation*} where $A$ and the initial values $x_{-i}$, $y_{-i}$,
$z_{-i}$, for $i=0,1,...,m$, are positive real numbers.
