Global Behavior of a Rational Recursive Sequence

Abstract

In this paper, we study the global behavior of the nonnegative equilibrium points of the difference equation

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

where \(a\), \(b\), and \(c\) are nonnegative parameters, initial conditions are nonnegative real numbers, and \(k\) and \(l\) are nonnegative integers, with \(l \leq k+1\).