Vitolo, Renato and Glendinning, Paul and Gallas, Jason A.C. (2011) Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. [MIMS Preprint]
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Abstract
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. We show that spirals associated with periodicity hubs emerge/accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.
| Item Type: | MIMS Preprint |
|---|---|
| Additional Information: | CICADA |
| Uncontrolled Keywords: | homoclinic, hub |
| Subjects: | PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems |
| Depositing User: | Professor Paul Glendinning |
| Date Deposited: | 04 Jul 2011 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1645 |
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