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

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.