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Global bifurcations of a multi-stable nonlinear oscillator

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Abstract

In this paper, we focus on the bifurcation analysis of a multi-stable nonlinear oscillator. This oscillator exhibits multiple equilibrium configurations depending on the parameter of a mechanical model. It is shown that the equilibrium curve undergoes multiple fold bifurcations, a supercritical pitchfork bifurcation, multiple discontinuous bifurcations, and multiple hysteresis bifurcations. Additionally, multiple solutions and different forms of bifurcation are observed for certain parameter values. Moreover, different response orbits under different initial conditions are emphasized by adopting the generalized cell mapping method.

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 11772144 and 11872188).

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Authors and Affiliations

  1. College of Physics, Liaoning University, Shenyang, 110036, China

    Chang Liu

  2. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, China

    Wen-An Jiang

  3. School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Liqun Chen

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  1. Chang Liu
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  2. Wen-An Jiang
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Correspondence to Wen-An Jiang.

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Liu, C., Jiang, WA. & Chen, L. Global bifurcations of a multi-stable nonlinear oscillator. Arch Appl Mech 93, 1149–1165 (2023). https://doi.org/10.1007/s00419-022-02319-7

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