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arXiv · 1601.02078

Solution Form of a Higher Order System of Difference Equation and Dynamical Behavior of Its Special Case

Nabila Haddad·Nouressadat Touafek·Julius Fergy T. Rabago
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Abstract

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}}{αx_{n-k}^{p}+βx_{n}}, \quad n, p \in \mathbb{N}_{0},\ k\in \mathbb{N}, \end{equation*} where the coefficients $a, b, α, β$ 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 results exhibited in the paper.

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Nabila Haddad, Nouressadat Touafek, Julius Fergy T. Rabago. 2016-03-27. Solution Form of a Higher Order System of Difference Equation and Dynamical Behavior of Its Special Case. https://doi.org/10.1002/mma.4248

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