Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equations
A framework for the occurrence of the nonresonant Hopf-Hopf bifurcation in an NFDE with parameters is established. The normal form up to the third order is obtained. Then the framework is applied to a Van der Pols equation with extended delayed feedback. Hopf-Hopf points are identified and the normal forms are calculated. A bifurcation diagram is derived to see that a rich dynamics such as periodic solutions, quasi-periodic solutions, even chaos may occur as the parameter values fall in the corresponding parameter regions.
neutral functional differential equations
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