| Abstrakt: |
This paper focuses on bursting behaviors of a Mathieu–van der Pol oscillator excited by low-frequency parametric and external excitations, where two novel bursting modes (namely cascaded bursting oscillations and non-cascaded bursting oscillations) are presented. In particular, the folds induced by the extreme values of the slow variable and the shape of the equilibrium branches are found on the quiescent state vibrations in two bursting patterns. We find that the spiking state vibrations can be induced by the subcritical Hopf bifurcations, supercritical Hopf bifurcations, and limit cycle fold bifurcations, and these three different types of the spiking state attractors can be found simultaneously with the variation of the positive integer ratio n. For the cascaded bursting, more and more large-amplitude limit cycles can be observed with the increase of n, leading to a greater number of the spiking states, while for the non-cascaded bursting, only one large-amplitude limit cycle can be found. In addition, we show that the spiking state attractors cannot be created by the small-amplitude limit cycles due to the Hopf bifurcation delay. [ABSTRACT FROM AUTHOR] |
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