Global Behavior of a Fourth Order Rational Difference Equation

R. Abo-Zeid, M. A. Al-Shabi

Abstract

In this paper, we investigate the global stability, periodic nature, and the oscillation of solutions of the difference equation \[x_{n+1}=\frac{Ax_{n-3}}{B+Cx_{n-2}^{2}},\qquad n=0,1,2,\ldots\] where $A,C,B>0$ and the initial conditions $x_{-3},x_{-2},x_{-1},x_0$ are nonnegative real numbers. We show that under certain conditions unbounded solutions will be obtained.