Table of Content
Local stability
Open AccessArticleBehavior and formula of the solutions of rational difference equations of order six
E. M. Elsayed, H. Malaikah and J. G. AL-Juaid*
Annals of Communications in Mathematics 2023,
6 (2),
72-85
DOI: https://doi.org/10.62072/acm.2023.060201
ABSTRACT.This paper is devoted to find the form of the solution of the following rational difference equation:\[x_{n+1}=\frac{x_{n-3}x_{n-5}}{x_{n-1}\left( \pm 1 \pm x_{n-3}x_{n-5} \right)},\]where the initial conditions \( x_{-5}, x_{-4}, x_{-3}, x_{-2}, x_{-1}, x_{0} \) are arbitrary non-zero real numbers. Also, we study the behavior of the solutions.




