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

\(x_{n+1} = \frac{Ax_{n-2l}}{B+C \prod\limits_{i=0}^{2k}x_{n-i}}, n=0,1,\ldots ,\)

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