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Zbl 1076.34087
Liao, Xiaofeng
Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays. (English)
[J] Chaos Solitons Fractals 23, No. 3, 857-871 (2005). ISSN 0960-0779

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.
[Jan Sieber (Bristol)]

MSC 2000:: *34K18 Bifurcation theory of functional differential equations
34K19 Invariant manifolds
34K13 Periodic solutions of functional differential equations

Keywords: van-der-Pol equation; delay differential equation; Hopf bifurcation; resonances

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