On the Dynamics of a Higher Order Nonlinear System of Difference Equations

Abstract

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.