Global Behavior of a Higher Order Difference Equation

Abstract

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

$x_{n+1}=\frac{A{x}_{n-2l}}{B+C\prod _{i=0}^{2k}{x}_{n-i}},n=0,1,\dots ,$

where $A$, $B$, $C$ are nonnegative parameters, initial conditions are nonnegative real numbers, and $k$, $l$ are nonnegative integers, $l\le k$. Also, we derive solutions of some special cases of this equation.