Gallas J, Vitolo R, Glendinning P (2011)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2011
Book Volume: 84
Pages Range: 016216
Journal Issue: 1
DOI: 10.1103/PhysRevE.84.016216
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 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.
APA:
Gallas, J., Vitolo, R., & Glendinning, P. (2011). Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. Physical Review E, 84(1), 016216. https://dx.doi.org/10.1103/PhysRevE.84.016216
MLA:
Gallas, Jason, Renato Vitolo, and Paul Glendinning. "Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows." Physical Review E 84.1 (2011): 016216.
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