Further properties of the rational recursive sequence xn + 1 = axn - 1 / (b + cxnxn - 1)

Abstract

In this paper we consider the difference equation $x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...(E)$ with positive parameters $a$ and $c$, negative parameter $b$ and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation $\text{(E)}$.