Multistability and Torus Reconstruction in a DC–DC Converter With Multilevel Control

Zhanybai T. Zhusubaliyev, Erik Mosekilde, Elena V. Pavlova

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By virtue of their limited size and relatively low costs, multilevel dc-dc converters have come to play an important role in modern industrial power supply systems. When operating in a regime of high corrector gain, such converters can display a variety of new dynamic phenomena associated with the appearance of additional oscillatory modes. Starting in a state where four pairs of stable and unstable period-6 cycles coexist with the basic period-1 cycle, the paper describes a sequence of smooth and nonsmooth bifurcations through which the cycles and their basins of attraction transform as the output voltage is increased. The paper also describes the birth of a multilayered resonance torus through a transverse pitchfork bifurcation of the saddle cycle on an ordinary resonance torus.
Original languageEnglish
JournalI E E E Transactions on Industrial Informatics
Issue number4
Pages (from-to)1937-1946
Publication statusPublished - 2013


  • bifurcation
  • DC-DC power convertors
  • oscillations
  • Power, Energy and Industry Applications
  • Signal Processing and Analysis


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