Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator

Xindong Ma, Yue Yu and Lifeng Wang

Applied Mathematics and Computation, 2021, vol. 411, issue C

Abstract: The intent of this work is to explore the generation mechanism of four mixed-mode vibration types triggered by the pitchfork bifurcation delay phenomenon in a driven van der Pol-Duffing oscillator. The four mixed-mode vibration types can be named “delayed sup-pitchfork/sup-Hopf” type for Homoclinic connection, symmetric “delayed sup-pitchfork/sup-Hopf” type, “point/point” type for delayed sup-pitchfork and “delayed sup-pitchfork/delayed Homoclinic” type, respectively. Our study proves that the pitchfork bifurcation delay phenomenon deserves a prominent role in the occurrence of the four mixed-mode vibration types, which enriches the dynamical behaviors of the bifurcation delay phenomenon as well as the possible routes to mixed-mode vibrations.

Keywords: Mixed-mode vibration; Pitchfork bifurcation delay; Van der Pol-Duffing oscillator; Slow-fast analysis (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006111

DOI: 10.1016/j.amc.2021.126522

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