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

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

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