Some remarks on the Melnikov function (Q2778478)
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scientific article; zbMATH DE number 1716051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on the Melnikov function |
scientific article; zbMATH DE number 1716051 |
Statements
2 April 2002
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Melnikov function
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residues
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Fourier coefficients
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bifurcation
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Some remarks on the Melnikov function (English)
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The authors study the system NEWLINE\[NEWLINE x'=f(x)+\varepsilon h(t+\alpha,x,\varepsilon), NEWLINE\]NEWLINE where \(\varepsilon\) is a small parameter. It is assumed that if \(\varepsilon=0\), then the system has a nondegenerate homoclinic solution \(\phi(t)\). The Melnikov function \(M(\alpha)\) is studied in the case where \(\phi(t)=\Phi(e^t)\) for a rational function \(\Phi\). The authors also study the second-order Melnikov function \(M_2(\alpha)\), i.e., the coefficient at \(\varepsilon^2/2\) in the expansion of the bifurcation function.
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