| Citation: |
Merve Kara, Yasin Yazlik. ON THE SOLUTIONS OF THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS VIA RECURSIVE RELATIONS OF ORDER TWO AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 736-753. doi: 10.11948/20210305
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ON THE SOLUTIONS OF THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS VIA RECURSIVE RELATIONS OF ORDER TWO AND APPLICATIONS
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Abstract
In this paper, we show that the following three-dimensional system of difference equations
$ \begin{equation*} x_{n+1}=\frac{y_{n}y_{n-2}}{bx_{n-1}+ay_{n-2}}, \ y_{n+1}=\frac{z_{n}z_{n-2}}{dy_{n-1}+cz_{n-2}}, \ z_{n+1}=\frac{x_{n}x_{n-2}}{fz_{n-1}+ex_{n-2}}, \end{equation*} $
for $n\in \mathbb{N}_{0}$, where the parameters a, b, c, d, e, f and the initial values $x_{-i}$, $y_{-i}$, $z_{-i}$, $i \in \{0,1,2\}$, are real numbers, can be solved, extending further some results in literature. Also, we determine the forbidden set of the initial values by using obtained formulas. Finally, some applications concerning aforementioned system of difference equations are given.
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Keywords:
- System of difference equations /
- explicit solution /
- forbidden set
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References
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Merve Kara, Yasin Yazlik. ON THE SOLUTIONS OF THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS VIA RECURSIVE RELATIONS OF ORDER TWO AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 736-753. doi: 10.11948/20210305
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