In this paper we consider the difference equation\begin{equation}\label{E}\tag{$E$}x_{n+1}=\frac{ax_{n-1}}{b+cx_nx_{n-1}},\quad n=0,1,\ldots\end{equation}with positive parameters and nonnegative initial conditions. We use the explicit formula for the solutions of equation (\ref{E}) in investigating their behavior.
@article{9,
title = {On the rational recursive sequence $x\_{n+1}=\frac{ax\_{n-1}}{b+cx\_nx\_{n-1}}$},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v43i0.9},
language = {EN},
url = {http://dml.mathdoc.fr/item/9}
}
Andruch-Sobiło, Anna; Migda, Małgorzata. On the rational recursive sequence $x_{n+1}=\frac{ax_{n-1}}{b+cx_nx_{n-1}}$. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v43i0.9. http://gdmltest.u-ga.fr/item/9/