The purpose of this paper aims to explore the mechanism of several different periodic bursting patterns based on a Mathieu-van der Pol-Duffing energy harvester with parameter excitation. These bursting patterns are categorized as ‘delayed supHopf/supHopf’ bursting, ‘delayed pitchfork/pitchfork’ bursting, ‘delayed Hopf-pitchfork/Hopf-pitchfork’ bursting, ‘delayed subHopf/supHopf’ bursting and ‘delayed subHopf/fold-cycle’ bursting, respectively. Since bursting oscillations can be created when the trajectory transfers between/among different attractors, which means the amplitude of bursting oscillations may be sufficient to overcome the potential barrier of the energy harvester, and thus it would have potential application value in energy harvesting.
In this paper, complex bursting patterns in a modified Rayleigh–van der Pol-Duffing oscillator(abbreviated as MRPDO) under the simultaneous effect of parametric and external excitations are given theoretically by fast-slow analysis method. Four different kinds of bursting oscillations, i.e. bursting of compound asymmetric “Homoclinic/Homoclinic” type, bursting of compound asymmetric “delayed Homoclinic/Homoclinic” type, bursting of compound “fold/delayed Homoclinic connection/supHopf-supHopf/supHopf” type and bursting of “fold/delayed Homoclinic” type, are studied. For bursting of compound “fold/delayed Homoclinic connection/supHopf-supHopf/supHopf” type, we explain the delay generation mechanism. Based on the characteristics of the Homoclinic-limit cycles, we propose the concepts of the approximate quiescent state and peculiar limit cycle attractor.
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