Long-term behavior of solutions of the difference equation \(x_{n+1}=x_{n - 1}x_{n - 2} - 1\) (Q624466)
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scientific article; zbMATH DE number 5848798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Long-term behavior of solutions of the difference equation \(x_{n+1}=x_{n - 1}x_{n - 2} - 1\) |
scientific article; zbMATH DE number 5848798 |
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Long-term behavior of solutions of the difference equation \(x_{n+1}=x_{n - 1}x_{n - 2} - 1\) (English)
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9 February 2011
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Summary: We investigate the long-term behavior of solutions of the following difference equation: \(x_{n+1}=x_{n-1}x_{n-2}-1\), \(n\in\mathbb N_0\), where the initial values \(x_{-2},x_{-1}\), and \(x_0\) are real numbers. Numerous fascinating properties of the solutions of the equation are presented.
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periodic solutions
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stability
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nonlinear difference equations
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long-term behavior
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