The Dynamics of The Difference Equation $x_{n+1}=\frac{\alpha x_{n-k}}{\beta +\gamma x_{n-(k+1)}^p}$

Abstract

In this paper, we investigate the global behavior of the difference equation

$$x_{n+1}=\frac{\alpha x_{n-k}}{\beta +\gamma x_{n-(k+1)}^p},\text{n=1,2,}\dots$$

with non-negative parameters and non-negative initial conditions, where $k$ is an odd number.