Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
| Autor: | Merve Kara, Yasin Yazlik |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematica Slovaca. 71:1133-1148 |
| ISSN: | 1337-2211 0139-9918 |
| DOI: | 10.1515/ms-2021-0044 |
| Popis: | In this paper, we show that the following three-dimensional system of difference equations x n + 1 = y n x n − 2 a x n − 2 + b z n − 1 , y n + 1 = z n y n − 2 c y n − 2 + d x n − 1 , z n + 1 = x n z n − 2 e z n − 2 + f y n − 1 , n ∈ N 0 , $$\begin{equation*}x_{n+1}=\frac{y_{n}x_{n-2}}{ax_{n-2}+bz_{n-1}}, \quad y_{n+1}=\frac{z_{n}y_{n-2}}{cy_{n-2}+dx_{n-1}}, \quad z_{n+1}=\frac{x_{n}z_{n-2}}{ez_{n-2}+fy_{n-1}}, \quad n\in \mathbb{N}_{0},\end{equation*}$$ where the parameters a, b, c, d, e, f and the initial values x −i , y −i , z −i , i ∈ {0, 1, 2}, are complex numbers, can be solved, extending further some results in the literature. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, an application concerning a three-dimensional system of difference equations are given. |
| Databáze: | OpenAIRE |
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