The Global behavior of a certain difference polynomial equation

Abstract

In this paper we will present the Julia set and the global behavior of a polynomial second order
difference equation of type
x_{n+1}=ax_{n}^{m}x_{n-1}+ax_{n-1}^{m+1}+bx_{n-1}
where m from  N, a > 0 and b >= 0 with non-negative initial conditions.