Global asymptotic stability of a family of difference equations (Q5919976)
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scientific article; zbMATH DE number 5580122
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global asymptotic stability of a family of difference equations |
scientific article; zbMATH DE number 5580122 |
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Global asymptotic stability of a family of difference equations (English)
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17 July 2009
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For the difference equation \[ x_n= [(f_1f_2f_3+ f_1+ f_2+ f_3+ h)/(f_1f_2+ f_1f_3+ f_2f_3+ g+ h)](x_{n-1},\dots, x_{n-r}) \] with continuous functions \(f_1,f_2,f_3,g,h: (\mathbb{R}_+)^r\to \mathbb{R}_+\) and positive initial values, sufficient conditions are given such that 1 is a globally asymptotic stable equilibrium.
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rational difference equation
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globally asymptotic stability
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equilibrium
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