MMN-4248

# On a solvable system of difference equations of sixth-order

*Dilek Karakaya*;

*Yasin Yazlik*;

*Merve Kara*;

## Abstract

In this paper, we study the following two-dimesional system of difference equations
\begin{equation*}
x_{n}=\frac{x_{n-4}y_{n-5}x_{n-6}}{y_{n-1}x_{n-2}\left(a+b y_{n-3}x_{n-4}y_{n-5}x_{n-6} \right)}, \ y_{n}=\frac{y_{n-4}x_{n-5}y_{n-6}}{x_{n-1}y_{n-2}\left(c+d x_{n-3}y_{n-4}x_{n-5}y_{n-6} \right)}, \ n\in \mathbb{N}_{0},
\end{equation*}%
where the parameters $a, b, c, d$ and the initial values $x_{-i},y_{-i}$, $i \in \{1,2,3,4,5,6\}$, are real numbers. We show that some solvable subclasses of the class of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of difference equations.

Vol. 24 (2023), No. 3, pp. 1405-1426

DOI: 10.18514/MMN.2023.4248