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Turkish Journal of Mathematics

DOI

10.3906/mat-1902-24

Abstract

In this paper, we show that the following higher-order system of nonlinear difference equations, $ x_{n}=\frac{x_{n-k}y_{n-k-l}}{y_{n-l}\left( a_{n}+b_{n}x_{n-k}y_{n-k-l}\right)}, \ y_{n}=\frac{y_{n-k}x_{n-k-l}}{x_{n-l}\left( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}, \left(b_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\alpha_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\beta_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}, \ y_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case $k=2, l=k$.

Keywords

System of nonlinear difference equations, solution of system of difference equations in closed form, asymptotic behavior

First Page

1533

Last Page

1565

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