Abstract
A generalization of the van der Pol oscillator, in which a cubic non-linearity in the restoring force is considered, has been studied. For very small values of the cubic parameter, different chaotic transitions take place, via period-doubling, saddle-node bifurcations and crises, which restore the symmetry of the chaotic attractor. For larger values of the parameter a period-adding sequence of saddle-node bifurcations and the scaling laws that rule them are found. When negative values of the cubic parameter are considered, birfucations via hysteresis following a period-adding sequence are found. Finally, it has been found that there is a strong sensitivity to very small modifications of some system parameters.
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