Fourteen limit cycles in a seven-degree nilpotent system (Q2015500)
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scientific article; zbMATH DE number 6306798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourteen limit cycles in a seven-degree nilpotent system |
scientific article; zbMATH DE number 6306798 |
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Fourteen limit cycles in a seven-degree nilpotent system (English)
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23 June 2014
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Summary: Center conditions and the bifurcation of limit cycles for a seven-degree polynomial differential system in which the origin is a nilpotent critical point are studied. Using the computer algebra system Mathematica, the first 14 quasi-Lyapunov constants of the origin are obtained, and then the conditions for the origin to be a center and the 14th-order fine focus are derived, respectively. Finally, we prove that the system has 14 limit cycles bifurcated from the origin under a small perturbation. As far as we know, this is the first example of a seven-degree system with 14 limit cycles bifurcated from a nilpotent critical point.
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center conditions
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bifurcation of limit cycles
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computer algebra system
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\texttt{Mathematica}
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0.8891887
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0.8764931
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0.86844003
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0.86591494
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0.8590841
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