On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\) (Q949118)
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scientific article; zbMATH DE number 5354281
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\) |
scientific article; zbMATH DE number 5354281 |
Statements
On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\) (English)
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20 October 2008
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The solutions of the difference equation in the title with positive coefficients and positive initial values are studied with respect to persistence and 2-periodicity. Moreover, conditions are given such that the equilibrium is locally asymptotically stable resp. a global attractor.
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rational difference equation
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persistence
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periodicity
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stability
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global attractor
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