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Quasiperiodicity and torus breakdown in a power electronic dc/dc converter

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  • Zhusubaliyev, Zhanybai T.
  • Soukhoterin, Evgeniy
  • Mosekilde, Erik

Abstract

This paper discusses the mechanisms of torus formation and torus destruction in a dc/dc converter with relay control and hysteresis. We establish a chart of the dynamical modes in the input voltage versus load resistance parameter plane. This chart displays several different torus bifurcations along with their associated resonance tongues where periodic dynamics is observed. We show how a quintruple-turn torus is transformed into a single-turn torus in a homoclinic bifurcation and examine different mechanisms of torus destruction (via horseshoe formation and through period doubling). Particular emphasis is paid to following the changes of the stable and unstable manifolds in detail.

Suggested Citation

  • Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.
    • Handle: RePEc:eee:matcom:v:73:y:2007:i:6:p:364-377
    DOI: 10.1016/j.matcom.2006.06.021
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    References listed on IDEAS

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    1. Gallegati, M. & Gardini, L. & Puu, T. & Sushko, I., 2003. "Hicks’ trade cycle revisited: cycles and bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 505-527.
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    Cited by:

    1. Zhang, Hao & Yang, Xiao-Ping & Ma, Xi-Kui & Zheng, Feng, 2011. "Theoretical and experimental investigation of bidirectional Hopf bifurcations in cascade DC–DC buck converters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 540-557.
    2. Zhusubaliyev, Zhanybai T. & Mosekilde, Erik, 2015. "Multistability and hidden attractors in a multilevel DC/DC converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 32-45.
    3. Gardini, Laura & Tramontana, Fabio & Sushko, Iryna, 2010. "Border collision bifurcations in one-dimensional linear-hyperbolic maps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 899-914.
    4. Dal Forno, Arianna & Merlone, Ugo, 2013. "Border-collision bifurcations in a model of Braess paradox," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 1-18.
    5. Fabio TRAMONTANA & Laura GARDINI & Puu TONU, 2008. "Cournot Duopoly with Capacity Limit Plants," Working Papers 314, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Gavagsaz-Ghoachani, R. & Phattanasak, M. & Martin, J.-P. & Pierfederici, S. & Davat, B., 2013. "Predicting the onset of bifurcation and stability study of a hybrid current controller for a boost converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 91(C), pages 262-273.

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