Stability and convergence of a higher order rational difference Equation
Dynamical Systems
2011-04-25 v1
Abstract
In this paper the asymptotic stability of equilibria and periodic points of the following higher order rational difference Equation x_{n+1} =(alpha x_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters ?alpha, betta, and gamma are positive real numbers, and the initial conditions x_{-k}, ..., x_{0} are given arbitrary real numbers. The forbidden set of this equation is found and then, the order reduction method is used to facilitate the analysis of its asymptotic dynamics
Cite
@article{arxiv.1104.4402,
title = {Stability and convergence of a higher order rational difference Equation},
author = {Hamid Gazor and Saeed Parvandeh},
journal= {arXiv preprint arXiv:1104.4402},
year = {2011}
}