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Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems

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  • Brandon, Quentin
  • Ueta, Tetsushi
  • Fournier-Prunaret, Danièle
  • Kousaka, Takuji

Abstract

In this paper, we consider a numerical method for the bifurcation analysis method of nonlinear piecewise-smooth systems. While linear piecewise-smooth systems can be analyzed rigorously, nonlinear piecewise-smooth systems cannot lead to an analytical solution. Derived from both continuous and discrete system analysis approaches, our method uses a Poincaré map to transform the results of partial analysis over the continuous components into those issued from a discrete mapping. We then apply conventional methods in order to find critical parameter values and obtain bifurcation diagrams in the parameter space. The numerical procedure is fully described and illustrated by the analysis results of various versions of the Alpazur oscillator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:187-201
    DOI: 10.1016/j.chaos.2008.11.013
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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. Kousaka, Takuji & Ueta, Tetsushi & Ma, Yue & Kawakami, Hiroshi, 2006. "Control of chaos in a piecewise smooth nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1019-1025.
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    1. 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.

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