The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\) (Q2463925)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\) |
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The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\) (English)
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6 December 2007
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For the equation in the title with \(0< k< m\) it is shown that all positive solutions converge to the equilibrium 1. Two conjectures concerning the asymptotic stability for positive solutions of more general difference equations are given.
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asymptotic stability
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symmetry
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positive solutions
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