On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\) (Q1767384)
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scientific article; zbMATH DE number 2143261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\) |
scientific article; zbMATH DE number 2143261 |
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On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\) (English)
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10 March 2005
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It is shown that for arbitrary real \(\alpha\) the equation in the title has a monotone solution converging to the equilibrium \(\alpha-1\). Under additional assumptions, the equilibrium is globally asymptotically stable and a global attractor. The authors also give conditions such that all solutions are bounded, all solutions are chaotic, resp. such that there exists a 2-periodic solution.
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rational difference equation
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global asymptotic stability
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global attractor
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bounded solution
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chaotic solution
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periodic solutions
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convergence
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