Feedforward attractor targeting for non-linear oscillators using a 
dual-frequency driving technique

Hegedűs, F.; Krähling, P.; Aron, Marcel; Lauterborn, W.; Mettin, R.; Parlitz, Ulrich

doi:10.1063/5.0005424

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Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique

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Aron, Marcel
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Parlitz, Ulrich
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Hegedűs, F., Krähling, P., Aron, M., Lauterborn, W., Mettin, R., & Parlitz, U. (2020). Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30: 073123. doi:10.1063/5.0005424.

Cite as: https://hdl.handle.net/21.11116/0000-0006-FEC2-1

Abstract

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency–amplitude
parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To
illustrate this approach, it is applied to the Keller–Miksis equation describing the radial dynamics of a single spherical gas bubble placed in
an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper
selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the
trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The
transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium
state (absence of external driving) of the system.