On the Dynamics of a Recursive Sequence

Abstract

We describe the global behavior of the nonnegative equilibrium points of the difference equation

\[x_{n+1} = \frac{ax_{n -p}}{b+c \prod\limits_{i=0}^{k} x_{n-(2i+1)}},n=0,1,\ldots,\]

where \(k,p \in \mathbb{N}\), parameters \(a,b,c\) and initial conditions are nonnegative real numbers.