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Broken Farey tree and fractal in a hexagonal centrifugal governor with a spring

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  • Rao, Xiao-Bo
  • Chu, Yan-Dong
  • Chang, Ying-Xiang
  • Zhang, Jian-Gang

Abstract

The global dynamical behaviors of a hexagonal centrifugal governor with a spring are expanded in this paper. The high-definition resolution phase diagrams are used to identify how the complex mode-locking behaviors arise with the parameters changed. By calculating the rotation number, it is unfolded that the interesting “Devils staircase” is presented with the parameter changed, meanwhile, the mode-locking structure is organized according to the broken Farey tree sequence. In addition, the fractal structure with self-similarity can also be observed in this system.

Suggested Citation

  • Rao, Xiao-Bo & Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang, 2018. "Broken Farey tree and fractal in a hexagonal centrifugal governor with a spring," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 251-255.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:251-255
    DOI: 10.1016/j.chaos.2018.01.015
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    Cited by:

    1. Yang, Yanling & Wang, Qiubao, 2023. "Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Liu, Cui & He, Rui-chun & Zhou, Wei & Li, Hui, 2021. "Dynamic analysis of airline bidding game based on nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Rao, Xiao-Bo & Zhao, Xu-Ping & Chu, Yan-Dong & Zhang, Jian-Gang & Gao, Jian-She, 2020. "The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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