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Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays. (English) Zbl 1076.34087
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.
MSC:
34K18Bifurcation theory of functional differential equations
34K19Invariant manifolds (functional-differential equations)
34K13Periodic solutions of functional differential equations