Normal forms of quadratic vector fields and the Shi Songling equation (Q610334)
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scientific article; zbMATH DE number 5824114
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Normal forms of quadratic vector fields and the Shi Songling equation |
scientific article; zbMATH DE number 5824114 |
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Normal forms of quadratic vector fields and the Shi Songling equation (English)
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8 December 2010
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The paper contains a method for the localization of limit cycles for planar vector fields with a weak focus. This method is applied to analyze a large domain on the phase plane for the Shi Songling example -- a quadratic vector field with at least four limit cycles. In a neighborhood of the singular point \(O(0,0)\) three very narrow annuli are obtained in each of which there is a unique limit cycle.
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quadratic system
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limit cycle
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bifurcation
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Hilbert's 16th problem
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