Abstract
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.
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