Dynamic behavior of a second-order nonlinearrational difference equation

Authors

YACINE HALIM
NOURESSADAT TOUAFEK
YASİN YAZLIK

DOI

10.3906/mat-1503-80

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.

Keywords

Global stability, difference equations, local asymptotic stability, periodicity

First Page

1004

Last Page

1018

Recommended Citation

HALIM, YACINE; TOUAFEK, NOURESSADAT; and YAZLIK, YASİN (2015) "Dynamic behavior of a second-order nonlinearrational difference equation," Turkish Journal of Mathematics: Vol. 39: No. 6, Article 18. https://doi.org/10.3906/mat-1503-80
Available at: https://journals.tubitak.gov.tr/math/vol39/iss6/18