Limit cycles of a class of polynomial vector fields in the plane (Q1106378)
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scientific article; zbMATH DE number 4061675
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limit cycles of a class of polynomial vector fields in the plane |
scientific article; zbMATH DE number 4061675 |
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Limit cycles of a class of polynomial vector fields in the plane (English)
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1986
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Examples giving negative answers to questions asked by \textit{D. E. Koditschek} and \textit{K. S. Narendra} (J. Differ. Equations 54, 181-195 (1984; Zbl 0498.34018)) are produced and a generalization of the theorem of Koditschek and Narendra is proved; the generalization consists of replacing a linear function f by a smooth homogeneous function which takes on both positive and negative values. Results of computer experiments are reported to show ``something of the shapes of the limit cycles to be expected from a system in the form considered.''
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polynomial vector fields
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planar systems
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limit cycles
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