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Non-quantum chirality and periodic islands in the driven double pendulum system

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  • Liu, Zeyi
  • Rao, Xiaobo
  • Gao, Jianshe
  • Ding, Shunliang

Abstract

The paper presents a systematic investigation of the dynamic complexities exhibited by a driven double pendulum system. By utilizing isospike diagrams in the frequency–amplitude control parameter space, a wide range of novel dynamical behaviors are explored. In addition to the well-known shrimp-shaped period island, the study uncovers various unique self-organizations, including the quint point where five distinct stable oscillatory phases coalesce, the eye of chaos characterized by a nested ring structure resulting from forward and reverse cascades, and innovative non-quantum chiral structures. The observed chiral structures in the double pendulum system exist in more diverse and generalized structure, challenging the notion that ring structures are necessary for their emergence. Furthermore, the study reports the experimental observation of a newly generated parabolic phase near the quint point, validating the phenomena observed through numerical calculations in experiments. These findings not only advance our understanding of the control parameter space topology for driven double pendulums but also lay the foundation for the exploration of innovative control strategies.

Suggested Citation

  • Liu, Zeyi & Rao, Xiaobo & Gao, Jianshe & Ding, Shunliang, 2023. "Non-quantum chirality and periodic islands in the driven double pendulum system," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011566
    DOI: 10.1016/j.chaos.2023.114254
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    References listed on IDEAS

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    1. Cabeza, Cecilia & Briozzo, Carlos A. & Garcia, Rodrigo & Freire, Joana G. & Marti, Arturo C. & Gallas, Jason A.C., 2013. "Periodicity hubs and wide spirals in a two-component autonomous electronic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 59-65.
    2. Cai, Qinlin & Zhu, Songye, 2021. "Applying double-mass pendulum oscillator with tunable ultra-low frequency in wave energy converters," Applied Energy, Elsevier, vol. 298(C).
    3. Xu, Lu & Chu, Yan-Dong & Yang, Qiong, 2020. "Novel dynamical Scenario of the two-stage Colpitts oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    5. Bishop, S.R. & Sofroniou, A. & Shi, P., 2005. "Symmetry-breaking in the response of the parametrically excited pendulum model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 257-264.
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