Journal
PHYSICS LETTERS A
Volume 380, Issue 9-10, Pages 1012-1022Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2016.01.022
Keywords
Bubble dynamics; Bifurcation structure; Nonlinear dynamics; Parameter continuation; Topology; Farey ordering
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Funding
- Hungarian Scientific Research Fund - OTKA [K81621]
- Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
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The topology of the stable periodic orbits of a harmonically driven bubble oscillator, the Rayleigh-Plesset equation, in the space of the excitation parameters (pressure amplitude and frequency) has been revealed numerically. This topology is governed by a hierarchy of two-sided Farey trees initiated from a unique primary structure defined also by a simple asymmetric Farey tree. The sub-topology of each of these building blocks is driven by a homoclinic tangency of a periodic saddle. This self-similar organisation is a suitable basis for a general description, since it is in good agreement with partial results obtained in other periodically forced oscillators and iterated maps. The applied ambient pressure in the model is near but still below Blake's critical threshold. Therefore, this paper is also a straightforward continuation of the work of Hegedus [1], who first found numerical evidence for the existence of stable, period I solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity. (C) 2016 Elsevier B.V. All rights reserved.
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