Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows.

  title={Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows.},
  author={Renato Vitolo and Paul Glendinning and Jason A. C. Gallas},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={84 1 Pt 2},
Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler's oscillator. We show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic… CONTINUE READING

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