Global Behavior of a Higher Order Rational Difference Equation


R. Abo-Zeid




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