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A computation method for non-autonomous systems with discontinuous characteristics

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  • Miino, Yuu
  • Ito, Daisuke
  • Ueta, Tetsushi

Abstract

We propose a computation method to obtain bifurcation sets of periodic solutions in non-autonomous systems with discontinuous properties. If the system has discontinuity for the states and/or the vector field, conventional methods cannot be applied. We have developed a method for autonomous systems with discontinuity by taking the Poincaré mapping on the switching point in the preceded study, however, this idea does not work well for some non-autonomous systems with discontinuity. We overcome this difficulty by extending the system to an autonomous system. As a result, bifurcation sets of periodic solutions are solved accurately with a shooting method. We show two numerical examples and demonstrate the corresponding laboratory experiment.

Suggested Citation

  • Miino, Yuu & Ito, Daisuke & Ueta, Tetsushi, 2015. "A computation method for non-autonomous systems with discontinuous characteristics," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 277-285.
    • Handle: RePEc:eee:chsofr:v:77:y:2015:i:c:p:277-285
    DOI: 10.1016/j.chaos.2015.06.014
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    Cited by:

    1. Miino, Yuu & Ueta, Tetsushi & Kawakami, Hiroshi, 2018. "Nonlinear resonance and devil’s staircase in a forced planer system containing a piecewise linear hysteresis," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 75-85.
    2. Ito, Daisuke & Asahara, Hiroyuki & Kousaka, Takuji & Ueta, Tetsushi, 2018. "Clock pulse modulation for ripple reduction in buck-converter circuits," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 138-145.
    3. Yuu Miino & Tetsushi Ueta, 2018. "Influence of Bifurcation Structures Revealed by Refinement of a Nonlinear Conductance in JosephsonJunction Element," Complexity, Hindawi, vol. 2018, pages 1-10, December.

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