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A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller-Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. Dur-Electronic supplementary material The online version of this article (

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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 organization 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 Hegedűs [1], who first found numerical evidence for the existence of stable, period 1 solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity.

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