Solvability of a system of nonlinear difference equations of higher order

Authors : Merve KARA, Yasin YAZLIK

Pages : 1533-1565

View : 12 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

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}\leftinsert ignore into journalissuearticles values( 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}\leftinsert ignore into journalissuearticles values( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right);}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\leftinsert ignore into journalissuearticles values(a_{n} \right);_{n\in \mathbb{N}_{0}}, \leftinsert ignore into journalissuearticles values(b_{n} \right);_{n\in \mathbb{N}_{0}}, \leftinsert ignore into journalissuearticles values(\alpha_{n} \right);_{n\in \mathbb{N}_{0}}, \leftinsert ignore into journalissuearticles values(\beta_{n} \right);_{n\in \mathbb{N}_{0}}$ 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