Turkish Journal of Mathematics
Abstract
This paper deals with the global attractivity of positive solutions of the second-order nonlinear difference equation \begin{equation*} x_{n+1}=\frac{ax_{n}^{k}+b\displaystyle\sum_{j=1}^{k-1}x_{n}^{j}x_{n-1}^{k-j}+cx_{n-1} ^{k}}{Ax_{n}^{k}+B\displaystyle\sum_{j=1}^{k-1}x_{n}^{j}x_{n-1}^{k-j}+Cx_{n-1}^{k}},\ k=3,4,...,\,n=0,1,...,\label{eq1} \end{equation*} where the parameters $a$, $b$, $c$, $A$, $B$, $C$ and the initial values $x_{0}$, $x_{-1}$ are arbitrary positive real numbers.
DOI
10.3906/mat-1503-80
Keywords
Global stability, difference equations, local asymptotic stability, periodicity
First Page
1004
Last Page
1018
Recommended Citation
HALIM, Y, TOUAFEK, N, & YAZLIK, Y (2015). Dynamic behavior of a second-order nonlinearrational difference equation. Turkish Journal of Mathematics 39 (6): 1004-1018. https://doi.org/10.3906/mat-1503-80
