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

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

Chaos, Solitons & Fractals, 2018, vol. 107, issue C, 251-255

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.

Keywords: Centrifugal governor; Farey tree; Quasi-periodic motion; Fractal structure; Rotation number; Devil’s staircase (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:107:y:2018:i:c:p:251-255

DOI: 10.1016/j.chaos.2018.01.015

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