The monotonicity of period function for the codimension four quadratic system \(Q_4\). (Q1864639)
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scientific article; zbMATH DE number 1884207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The monotonicity of period function for the codimension four quadratic system \(Q_4\). |
scientific article; zbMATH DE number 1884207 |
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The monotonicity of period function for the codimension four quadratic system \(Q_4\). (English)
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18 March 2003
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The author studies the codimension four quadratic system \[ \dot{z}=-iz+4z^2+2| z| ^{2}+(b+ic)\bar{z}^{2},\tag{\(Q_4\)} \] where \(b,c\in\mathbb{R}\), \(i^{2}=-1\), \(z=x+iy\) and \(| b+ic| =2\). The author investigates the period function \[ T(h):=\oint_{\Gamma_{h}}\,dt. \] The main result of the paper is that the period function of periodic trajectories of system (\(Q_{4}\)) is monotone.
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limit cycles
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quadratic systems
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Abelian integrals
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