On the solutions of a system of max-type difference equations

Abstract

In this paper, we give explicit formulas of the solutions of the system of max-type difference equations \[ x_{n+1}=\max \left\{ x_{n-1},\frac{x_{n}y_{n-1}}{y_{n-2}}\right\} ,\,y_{n+1}=\max \left\{ y_{n-1},\frac{y_{n}x_{n-1}}{x_{n-2}}\right\} , \] where $n\geq 0$ and the initial values are positive real numbers.