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

作者：

Highlights：

• The supercritical pitchfork bifurcation delay behavior is studied in a driven van der PolDuffing oscillator.

• Threshold values of the Homoclinic and Heteroclinic bifurcations related to the inhibition of the chaotic behaviors are determined by the Melnikov method.

• Four mixed-mode vibrations triggered by the pitchfork bifurcation delay, i.e. “delayed sup-pitchfork/sup-Hopf” mixed-mode vibration for Homoclinic connection, symmetric “delayed pitchfork/sup-Hopf” mixed-mode vibration, “point/point” mixed mode vibration for delayed sup-pitchfork and “delayed sup-pitchfork/delayed Homoclinic” mixed-mode vibration, are investigated.

• The dynamical evolutions among different mixed-mode vibration types are presented by a two-parameter bifurcation analysis.

摘要

•The supercritical pitchfork bifurcation delay behavior is studied in a driven van der PolDuffing oscillator.•Threshold values of the Homoclinic and Heteroclinic bifurcations related to the inhibition of the chaotic behaviors are determined by the Melnikov method.•Four mixed-mode vibrations triggered by the pitchfork bifurcation delay, i.e. “delayed sup-pitchfork/sup-Hopf” mixed-mode vibration for Homoclinic connection, symmetric “delayed pitchfork/sup-Hopf” mixed-mode vibration, “point/point” mixed mode vibration for delayed sup-pitchfork and “delayed sup-pitchfork/delayed Homoclinic” mixed-mode vibration, are investigated.•The dynamical evolutions among different mixed-mode vibration types are presented by a two-parameter bifurcation analysis.

论文关键词：Mixed-mode vibration,Pitchfork bifurcation delay,Van der Pol-Duffing oscillator,Slow-fast analysis

论文评审过程：Received 29 December 2020, Revised 24 May 2021, Accepted 8 July 2021, Available online 21 July 2021, Version of Record 21 July 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126522