MMN-3996

# Global dynamical behaviours and periodicity of a certain quadratic-rational difference equation with delay

*E. Tasdemir*;

*M. GĂ¶cen*;

*Y. Soykan*;

## Abstract

Our aim in this paper is to deal with the dynamics of following higher order
difference equation%
\begin{equation*}
x_{n+1}=A+B\frac{x_{n-m}}{x_{n}^{2}}
\end{equation*}%
where $A,B>0$, and initial values are positive, and $m=\{1,2,...\}$\textbf{.}
Furthermore, we discuss the periodicity, boundedness, semi-cycles, global
asymptotic stability of solutions of these equations. We also handle the
rate of convergence of solutions of these difference equations.

Vol. 23 (2022), No. 1, pp. 471-484

DOI: 10.18514/MMN.2022.3996