Global attractivity in a recursive sequence (Q702617)
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scientific article; zbMATH DE number 2128811
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global attractivity in a recursive sequence |
scientific article; zbMATH DE number 2128811 |
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Global attractivity in a recursive sequence (English)
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17 January 2005
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The authors consider the rational difference equation \[ x_n = (ax_{n-1} - bx_{n-2})/(c+x_{n-2}) \] with \(a\), \(b\), \(c>0\). The following subjects are addressed: local asymptotic stability of the two equilibria (stability by the first approximation); invariant intervals (``manifolds''); global attractivity of the equilibria.
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rational difference equation
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equilibria stability
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oscillatory behavior
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local asymptotic stability
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invariant intervals
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global attractivity
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recursive sequence
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exponential convergence
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semicycle
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