On a Higher-Order Systems of Difference Equations

Abstract

Our goal in this objective is to study the form of the solutions of a class of rational systems of difference equations:

$$x_{n+1}=\frac{y_{n-5}x_{n-8}}{y_{n-2}\left(1+y_{n-5}x_{n-8}\right)}, y_{n+1}=\frac{x_{n-5}y_{n-8}}{x_{n-2}(\pm1\pm x_{n-5}y_{n-8})}, n=0,1,...,$$

where the initial conditions $x_{-\alpha}$, $y_{-\alpha}$, $\alpha\in\{0,1,...,8\}$ are non-zero real numbers. Keywords: Difference equations, Systems of difference equations, Recursive sequences.