Torus bifurcations in multilevel converter systems

Zhanybai T. Zhusubaliyev, Erik Mosekilde, Olga O. Yanochkina

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This paper considers the processes of torus formation and reconstruction through smooth and nonsmooth bifurcations in a pulse-width modulated DC/DC converter with multilevel control. When operating in a regime of high corrector gain, converters of this type can generate structures of stable tori embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes. The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company.
Original languageEnglish
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
Pages (from-to)2343-2356
Publication statusPublished - 2011


  • Piecewise-smooth dynamical systems
  • Torus birth bifurcations
  • Quasiperiodicity
  • Border-collision bifurcations


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