Abstract
In this work we study the invariant sets which emerge from the zero-Hopf bifurcations that general Van der Pol-Duffing equations can exhibit. We provide sufficient conditions for the simultaneous bifurcation of three periodic solutions and two invariant torus from the origin of this system. We use recent results related to the averaging method in order to analytically obtain our results. We also provide numerical examples for all the analytical results that we provide.
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