Global stability of a rational difference equation (Q5919932)
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scientific article; zbMATH DE number 5192543
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global stability of a rational difference equation |
scientific article; zbMATH DE number 5192543 |
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Global stability of a rational difference equation (English)
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19 September 2007
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For the difference equation \(x_{n+1}=bx_n/(1+b_0x_n+\cdots+b_kx_{n-k})\) with positive coefficients and \(b>1\) it is proved that the positive equilibrium is a global attractor of all positive solutions and for \(b_1+\cdots+b_k<b_0\) globally asymptotically stable.
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global attractor
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global asymptotic stability
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positive equilibrium
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positive solutions
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