Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$

Abstract

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of all admissible solutions of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$, n=0,1,2,... where A, B, C are positive real numbers.

Keywords

• difference equation
• periodic solution
• globally asymptotically stable