Higher order limit cycle bifurcations from non-degenerate centers (Q440792)
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scientific article; zbMATH DE number 6068322
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher order limit cycle bifurcations from non-degenerate centers |
scientific article; zbMATH DE number 6068322 |
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Higher order limit cycle bifurcations from non-degenerate centers (English)
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19 August 2012
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Poincaré-Lyapunov constant
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limit cycle
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center problem
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Gröbner basis
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The paper is devoted to the computation of the Poincaré-Lyapunov constants and to the determination of their functionally independent number for the following systems NEWLINE\[NEWLINE \dot{x}=-y+P_n(x, y), \;\dot{y}=x+Q_n(x, y), NEWLINE\]NEWLINE where \(P_n\) and \(Q_n\) are homogeneous polynomials of degree \(n\). By means of center bifurcation, the author estimates the cyclicity of a unique singular point of focus-center type for different values of \(n\). The presented results are obtained by using the implementation worked out by C. Christopher which exploits Cartesian coordinates and the computer algebra system \texttt{Reduce}.
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