On the rational recursive sequence \(x_{n+1}=\frac{\alpha + \beta x_{n-k}}{\gamma-x_{n}}\) (Q1034965)
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scientific article; zbMATH DE number 5627266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rational recursive sequence \(x_{n+1}=\frac{\alpha + \beta x_{n-k}}{\gamma-x_{n}}\) |
scientific article; zbMATH DE number 5627266 |
Statements
On the rational recursive sequence \(x_{n+1}=\frac{\alpha + \beta x_{n-k}}{\gamma-x_{n}}\) (English)
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9 November 2009
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The positive solutions of the difference equation in the title with positive entries and positive initial values are studied with respect to asymptotic stability, periodicity and boundedness. Under certain conditions, the equilibrium is a global attractor, and its basin is determined.
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rational difference equation
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asymptotic stability
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periodicity
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boundedness
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global attractor
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basin
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