Solution form of a higher order system of difference equation and dynamical behavior of its special case
arXiv preprint arXiv:1601.02078, 2016•arxiv.org
The solution form of the system of nonlinear difference equations\begin {equation*} x_ {n+
1}=\frac {x_ {n-k+ 1}^{p} y_ {n}}{a y_ {nk}^{p}+ b y_ {n}},\y_ {n+ 1}=\frac {y_ {n-k+ 1}^{p} x_
{n}}{\alpha x_ {nk}^{p}+\beta x_ {n}},\quad n, p\in\mathbb {N} _ {0},\k\in\mathbb {N},\end
{equation*} where the coefficients $ a, b,\alpha,\beta $ and the initial values $ x_ {-i}, y_ {-i},
i\in\{0, 1,\ldots, k\} $ are real numbers, is obtained. Furthermore, the behavior of solutions of
the above system when $ p= 1$ is examined. Numerical examples are presented to illustrate …
1}=\frac {x_ {n-k+ 1}^{p} y_ {n}}{a y_ {nk}^{p}+ b y_ {n}},\y_ {n+ 1}=\frac {y_ {n-k+ 1}^{p} x_
{n}}{\alpha x_ {nk}^{p}+\beta x_ {n}},\quad n, p\in\mathbb {N} _ {0},\k\in\mathbb {N},\end
{equation*} where the coefficients $ a, b,\alpha,\beta $ and the initial values $ x_ {-i}, y_ {-i},
i\in\{0, 1,\ldots, k\} $ are real numbers, is obtained. Furthermore, the behavior of solutions of
the above system when $ p= 1$ is examined. Numerical examples are presented to illustrate …
The solution form of the system of nonlinear difference equations \begin{equation*} x_{n+1} = \frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\ y_{n+1} = \frac{y_{n-k+1}^{p}x_{n}}{\alpha x_{n-k}^{p}+\beta x_{n}}, \quad n, p \in \mathbb{N}_{0},\ k\in \mathbb{N}, \end{equation*} where the coefficients and the initial values are real numbers, is obtained. Furthermore, the behavior of solutions of the above system when is examined. Numerical examples are presented to illustrate the results exhibited in the paper.
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