On the global attractivity and the periodic character of a recursive sequence

Abstract

In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $x_{n+1} = ax_n + \frac{bx_{n-1}+cx_{n+2}}{dx_{n-1}+ex_{n+2}}, \quad n=0,1,\ldots,$, where the parameters $a$, $b$, $c$, $d$ and $e$ are positive real numbers and the initial conditions $x_{-2}$, $x_{-1}$ and $x_{0}$ are positive real numbers.