Melnikov function and Poincaré map (Q806133)
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scientific article; zbMATH DE number 4205452
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Melnikov function and Poincaré map |
scientific article; zbMATH DE number 4205452 |
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Melnikov function and Poincaré map (English)
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1988
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The following ODE is investigated: \(x''+g(x)=\epsilon \mu f(x,x')+\epsilon \delta h(x,x',\omega t)\) where \(h(x,x',\omega t)\) is periodic in t. A relationship between the Melnikov function and the Poincaré mapping is established and a new proof for the Melnikov method is given. Some illustrative examples are also presented.
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bifurcation
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Poincaré mapping
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Melnikov method
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