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

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.