On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\). (English) Zbl 0962.39004

Summary: We study the global stability, the boundedness character, and the periodic nature of the positive solutions of the difference equation \(x_{n+1}= \alpha+ x_{n-1}/x_n\), where \(\alpha \in[0, \infty)\), and where the initial conditions \(x_{-1}\) and \(x_0\) are arbitrary positive real numbers.


39A11 Stability of difference equations (MSC2000)
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