Opuscula Math.
26
, no. 3
(), 387-394
Opuscula Mathematica

# Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}

Abstract. In this paper we consider the difference equation $x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...\tag{E}$ with positive parameters $$a$$ and $$c$$, negative parameter $$b$$ and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation $$\text{(E)}$$.
Keywords: difference equation, explicit formula, positive solutions, asymptotic stability.
Mathematics Subject Classification: 39A10.