Qualitative behavior of a rational recursive sequence of second order

Abstract

We investigate the dynamics and stability behavior of the solutions of the second order nonlinear difference equation $$ x_{n+1}=ax_{n}+\frac {bx_{n}+cx_{n-1}}{d+ex_{n}x_{n-1}} $$ where the parameters $a$, $b$, $c$, $d$ and $e$ are positive real numbers and the initial conditions $x_{-1}$ and $x_{0}$ are positive real numbers.