Global attractivity of the recursive sequence \(x_{n+1}= \frac {\alpha- \beta x_{n-k}} {\gamma+ x_n}\) (Q1885081)
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scientific article; zbMATH DE number 2111253
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global attractivity of the recursive sequence \(x_{n+1}= \frac {\alpha- \beta x_{n-k}} {\gamma+ x_n}\) |
scientific article; zbMATH DE number 2111253 |
Statements
Global attractivity of the recursive sequence \(x_{n+1}= \frac {\alpha- \beta x_{n-k}} {\gamma+ x_n}\) (English)
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28 October 2004
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The main aim of this paper is to investigate the global attractivity of the recursive sequence \[ x_{n+1}=\frac{\alpha-\beta x_{n-k}}{\gamma+x_n} \] where \(\alpha,\beta,\gamma>0\) and \(k\) is a positive integer. Some sufficient conditions are given for global attractivity or locally asymptotically stable of the positive equilibrium point of this equation.
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difference equation
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asymptotic stability
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positive equilibrium
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0.99579954
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0.9912478
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0.9327897
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0.93274266
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0.9297954
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0.9236385
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0.9206659
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