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On a solvable system of difference equations via some number sequences | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 212، دوره 13، شماره 2، مهر 2022، صفحه 2611-2637 اصل مقاله (606.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26918.3451 | ||
| نویسندگان | ||
| Merve Kara* 1؛ Yasin Yazlik2 | ||
| 1Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman, Turkey | ||
| 2Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektacs Veli University, Nevsehir, Turkey | ||
| تاریخ دریافت: 30 فروردین 1401، تاریخ بازنگری: 30 خرداد 1401، تاریخ پذیرش: 08 تیر 1401 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Interlacing indices؛ solution؛ forbidden set؛ Fibonacci number؛ Pell number | ||
| مراجع | ||
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