Opuscula Math. 26, no. 3 (2006), 387-394
Opuscula Mathematica
Further properties of the rational recursive sequence \(x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}\)
Anna Andruch-Sobiło
Małgorzata Migda
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.
- Anna Andruch-Sobiło
- Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland
- Małgorzata Migda
- Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland
- Received: 2005-09-23.
