Global Behavior of a Higher Order Rational Difference Equation

Abstract

In this paper, we derive the forbidden set and discuss the global behavior of all solutions of the difference equation
$$x_{n+1}=\frac{Ax_{n-k}}{B- C\prod_{i=0}^kx_{n-i}},\qquad n=0,1,\ldots $$
where $A,B,C$ are positive real numbers and the initial conditions $x_{-k},...,x_{-1},x_0$
are real numbers.