Abstract
We consider a modified van der Pol–Duffing electronic circuit,focusing on the case where a Hopf-pitchfork bifurcation takes places.The analysis of this bifurcation is a simple way to detect andcharacterize purely three-dimensional behaviour (an oscillatory regimein three variables, quasiperiodic motion, etc.).
The normal formanalysis provides the classification of different kinds ofHopf-pitchfork bifurcation, organized according to some degeneratecases. One of these degenerate cases is analyzed, by considering acodimension-three unfolding of a reflectionally symmetric planar vectorfield. Later, the implications for three-dimensional flows arepresented. Unlike another degenerate Hopf-pitchfork bifurcationsexhibited by the system, the one studied here does not involvequasiperiodic behaviour, so that the complexity related to quasiperiodicmotion is not present.
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Algaba, A., Freire, E., Gamero, E. et al. A Tame Degenerate Hopf-Pitchfork Bifurcation in a Modified van der Pol–Duffing Oscillator. Nonlinear Dynamics 22, 249–269 (2000). https://doi.org/10.1023/A:1008328027179
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DOI: https://doi.org/10.1023/A:1008328027179