Abstract
The complex bursting dynamics of a mechanical oscillator under parametric and external forced excitations are investigated. When the frequencies of the forcing terms are much smaller than the natural frequency of the oscillator, excitations can be expressed as slow-varying variables and the oscillator is regarded as a smooth autonomous system. A new route to bursting dynamics called the pulse-shaped explosion (PSE) is then proposed. PSE is represented by a sharp change in the number of pulse-shaped signals corresponding to the transformation of system parameters. Four PSE-type bursting dynamics are analyzed based on the slow-fast analysis method: bursting dynamics of “supHopf/supHopf” form via “PSE/PSE” hysteresis loop, bursting dynamics of “supHopf/supHopf-PSE/supHopf” form via “PSE/PSE” hysteresis loop, bursting dynamics of “supHopf/supHopf-PSE/PSE” form via “PSE/PSE” hysteresis loop and bursting dynamics of “PSE/PSE-PSE/PSE” form via “PSE/PSE” hysteresis loop. In addition, two non-PSE-type bursting dynamics are also investigated: bursting dynamics of “supHopf/supHopf” form and bursting dynamics of “supHopf/supHopf-supHopf/supHopf” form. Our results strengthen the understanding of the PSE-type bursting oscillations and enrich the possible routes to complex bursting behaviors.
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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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This paper is supported by the National Natural Science Foundation of China (Grant Nos. 12002134 and 11972173).
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Ma, X., Zhao, H. & Bi, Q. Novel bursting dynamics and the mechanism analysis in a mechanical oscillator. Nonlinear Dyn 109, 1485–1499 (2022). https://doi.org/10.1007/s11071-022-07520-5
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DOI: https://doi.org/10.1007/s11071-022-07520-5