Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays (Q1771676)
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scientific article; zbMATH DE number 2158546
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays |
scientific article; zbMATH DE number 2158546 |
Statements
Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays (English)
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18 April 2005
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The article studies the van der Pol equation with time delays. First, it investigates the location, direction and frequency of Hopf bifurcations of the origin for a general odd \(C^4\) nonlinearity and two time delays by studying the characteristic equation and deriving the Hopf normal form on the local center manifold. Then, the author studies double Hopf bifurcations for the case of a single delay, finding that they all have resonances.
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van-der-Pol equation
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delay differential equation
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Hopf bifurcation
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resonances
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