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Hysteresis suppression and synchronization near 3:1 subharmonic resonance

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  • Fahsi, Abdelhak
  • Belhaq, Mohamed

Abstract

Effect of a high-frequency excitation on hysteresis and synchronization area in a forced van der Pol–Duffing oscillator near the subharmonic 3:1 resonance is analyzed. By means of perturbation techniques, the 3:1 resonance area and the quasiperiodic modulation domain are captured. The results shown that adding a high-frequency excitation causes the backbone curves to shift and to bend from softening to hardening. The results also reveal that a high-frequency excitation significantly affects the resonance and the synchronization zones. Further, jump phenomenon occurring in a certain range of the forcing frequency suggesting that hysteresis near the 3:1 subharmonic resonance cannot be ignored in practical applications.

Suggested Citation

  • Fahsi, Abdelhak & Belhaq, Mohamed, 2009. "Hysteresis suppression and synchronization near 3:1 subharmonic resonance," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1031-1036.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1031-1036
    DOI: 10.1016/j.chaos.2009.02.043
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    References listed on IDEAS

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    1. Bourkha, Rachid & Belhaq, Mohamed, 2007. "Effect of fast harmonic excitation on a self-excited motion in Van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 621-627.
    2. Sah, Simohamed & Belhaq, Mohamed, 2008. "Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1489-1496.
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