Global Behavior of a Rational Difference Equation with Quadratic Term

R. Abo-Zeid

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of all solutions of the difference equation $x_{n+1} = \frac{ax_{n}x_{n-1}}{bx_{n}-cx_{n-2}},\qquad n=0,1,\dots$ where $a,b,c$ are positive real numbers and the initial conditions $x_{-2},x_{-1},x_{0}$ are real numbers.