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Strange Nonchaotic Attractors And Multistability In A Two-Degree-Of-Freedom Quasiperiodically Forced Vibro-Impact System

Author

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  • GAOLEI LI

    (Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China)

  • YUAN YUE

    (Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China)

  • CELSO GREBOGI

    (��Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK)

  • DENGHUI LI

    (��School of Mathematics and Statistics, Hexi University, Zhangye 734000, P. R. China)

  • JIANHUA XIE

    (�School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China)

Abstract

In this work, we initially study the strange nonchaotic dynamics of a two-degree-of-freedom quasiperiodically forced vibro-impact system. It is shown that strange nonchaotic attractors (SNAs) occur between two chaotic regions, but not between the quasiperiodic region and the chaotic one. Subsequently, we mainly focus on the abundant multistability in the system, especially the coexistence of SNAs and quasiperiodic attractors. Besides, the coexistence of quasiperiodic attractors of different frequencies, and the coexistence of quasiperiodic attractors and chaotic attractors are also uncovered. The basins of attraction of these coexisting attractors are obtained. The quasiperiodic attractor can transform into a chaotic attractor directly through torus break-up without passing through an SNA. The nonchaotic property of SNAs is verified by its maximal Lyapunov exponent, and the strange property of SNAs is described by its phase sensitivity, power spectrum, fractal structure, and rational approximations.

Suggested Citation

  • Gaolei Li & Yuan Yue & Celso Grebogi & Denghui Li & Jianhua Xie, 2021. "Strange Nonchaotic Attractors And Multistability In A Two-Degree-Of-Freedom Quasiperiodically Forced Vibro-Impact System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-13, June.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:04:n:s0218348x21501036
    DOI: 10.1142/S0218348X21501036
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    Cited by:

    1. Zhao, Yifan & Zhang, Yongxiang, 2023. "Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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