### On a solvable system of difference equations via some number sequences

Document Type : Research Paper

Authors

1 Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman, Turkey

2 Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektacs Veli University, Nevsehir, Turkey

Abstract

In this paper, we show that the following three-dimensional rational system of difference equations
\begin{equation*}
x_{n}=\frac{z_{n-1}z_{n-3}}{bx_{n-2}+az_{n-3}}, \ y_{n}=\frac{x_{n-1}x_{n-3}}{dy_{n-2}+cx_{n-3}}, \ z_{n}=\frac{y_{n-1}y_{n-3}}{fz_{n-2}+ey_{n-3}}, \ n\in \mathbb{N}_{0},
\end{equation*}
where the parameters $a, b, c, d, e, f$\ and the initial values $x_{-i},y_{-i},z_{-i}$, $i \in \{1,2,3\}$, are real numbers, can be solved in explicit form. In addition, the solutions of aforementioned systems according to the special cases of the parameters are given in closed form. Later, the forbidden set of the initial values for aforementioned system is described. Finally, an application and numerical examples to support our results are given.

Keywords

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###### Volume 13, Issue 2July 2022Pages 2611-2637
• Receive Date: 19 April 2022
• Revise Date: 20 June 2022
• Accept Date: 29 June 2022