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Bursters and quasi-periodic solutions of a self-excited quasi-periodic Mathieu oscillator

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  • Lakrad, Faouzi
  • Azouani, Abderrahim
  • Abouhazim, Nazha
  • Belhaq, Mohamed

Abstract

In this paper the conditions of occurrence of quasi-periodic (QP) solutions and bursting dynamics in a self-excited quasi-periodic Mathieu Oscillator are discussed. The quasi-periodic excitation consists of two periodic excitations; one with a very slow frequency and the other with a frequency resonant with the proper frequency of the oscillator. The fast dynamics are initially averaged. The complimentary quasi-static solutions of the modulation equations of amplitude and phase are determined and their stability is analyzed. Numerical simulations and power spectra are shown to complete the theoretical analysis.

Suggested Citation

  • Lakrad, Faouzi & Azouani, Abderrahim & Abouhazim, Nazha & Belhaq, Mohamed, 2005. "Bursters and quasi-periodic solutions of a self-excited quasi-periodic Mathieu oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 813-824.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:3:p:813-824
    DOI: 10.1016/j.chaos.2004.09.097
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