Global bifurcations of a multi-stable nonlinear oscillator

Liu, Chang; Jiang, Wen-An; Chen, Liqun

doi:10.1007/s00419-022-02319-7

Arch Appl Mech

2022

DOI: 10.1007/s00419-022-02319-7

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Global bifurcations of a multi-stable nonlinear oscillator

Chang Liu

Wen-An Jiang²,

Liqun Chen³

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2024

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Cited by 1 publication

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Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators

Sun,

Li,

Zhu

2024

J. Phys.: Conf. Ser.

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When appropriate parameters are selected, coupled SD oscillators can exhibit bistability, tristability, and even quadrastability. The presence of multiple potential wells introduces rich dynamical characteristics into these multi-stable systems. As a result, global dynamical analysis of quad-stable systems, particularly the study of sub-harmonic orbits, has garnered significant attention in recent years. This paper aims to investigate subharmonic motion in the quad-stable system of coupled SD oscillators and to establish a theoretical framework for Melnikov analysis of Type I subharmonic orbits. Based on the derived Melnikov function, the existence of Type I subharmonic orbits is verified. Finally, numerical simulation methods are employed to validate the proposed approach by plotting phase portrait, the time history diagram t − x and spectrum diagram.

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Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators

Sun,

Li,

Zhu

2024

J. Phys.: Conf. Ser.

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Global bifurcations of a multi-stable nonlinear oscillator

Cited by 1 publication

References 39 publications

Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators

Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators

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