Opuscula Math. 26, no. 3 (2006), 387-394
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.
About the authors ▼
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
About the article ▼
Received: 2005-09-23.
Cite this article as ▼
Anna Andruch-Sobiło, Małgorzata Migda, Further properties of the rational recursive sequence \(x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}\), Opuscula Math. 26, no. 3 (2006), 387-394,
http://dx.doi.org/10.7494/OpMath.2006.26.3.387.
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