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

Faouzi Lakrad, Abderrahim Azouani, Nazha Abouhazim and Mohamed Belhaq

Chaos, Solitons & Fractals, 2005, vol. 24, issue 3, 813-824

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:24:y:2005:i:3:p:813-824

DOI: 10.1016/j.chaos.2004.09.097

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