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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia et al. (Ultrasonics 49(8):605, 2009) revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that $$R_\mathrm{E} \omega $$ R E ω is kept constant....
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...
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