Zero-Hopf bifurcation in the general Van der Pol-Duffing equation (Q2159368)

This article investigates simultaneous bifurcations to periodic solutions and invariant tori emerging from different families of Zero-Hopf bifurcation boundaries of the general Van der Pol-Duffing equation with a cubic linearity. Using an advanced version of the averaging method, which is explained in a different article by the first author, it is shown that from the same bifurcation point three branches of periodic solutions and 2 families of tori can bifurcate. The authors also calculate the stability of these branches. Finally some of the emerging solutions are also computed numerically. It would have been interesting to get a fuller picture of the complicated ongoing dynamics and relations between the different solution branches by bifurcation diagrams.