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Bifurcation structure of chaotic attractor in switched dynamical systems with spike noise

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  • Matsuo, Akihito
  • Asahara, Hiroyuki
  • Kousaka, Takuji

Abstract

High-frequency ripple (spike noise) effects in the qualitative properties of DC/DC converter circuits. This study investigates the bifurcation structure of a chaotic attractor in a switched dynamical system with spike noise. First, we introduce the system dynamics and derive the associated Poincaré map. Next, we show the bifurcation structure of the chaotic attractor in a system with spike noise. Finally, we investigate the dynamical effect of spike noise in the existence region of the chaotic attractor compare with that of a chaotic attractor in a system with ideal switching. The results suggest that spike noise enlarges an invariant set and generates a new bifurcation structure of the chaotic attractor.

Suggested Citation

  • Matsuo, Akihito & Asahara, Hiroyuki & Kousaka, Takuji, 2012. "Bifurcation structure of chaotic attractor in switched dynamical systems with spike noise," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 795-804.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:795-804
    DOI: 10.1016/j.chaos.2012.02.011
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    References listed on IDEAS

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    1. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    2. Gardini, Laura & Tramontana, Fabio, 2011. "Border collision bifurcation curves and their classification in a family of 1D discontinuous maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 248-259.
    3. Brandon, Quentin & Ueta, Tetsushi & Fournier-Prunaret, Danièle & Kousaka, Takuji, 2009. "Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 187-201.
    4. Brianzoni, Serena & Michetti, Elisabetta & Sushko, Iryna, 2010. "Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 52-61.
    5. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.
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