Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving GPU accelerated topological analysis of a bubble in water

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 com...

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Veröffentlicht in:Nonlinear dynamics Jg. 94; H. 1; S. 273 - 293
Hauptverfasser: Hegedűs, Ferenc, Lauterborn, Werner, Parlitz, Ulrich, Mettin, Robert
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.10.2018
Schlagworte:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Original Paper
Vibration
Control of multistability
Nonlinear dynamics
Dual-frequency driving
GPU programming
Bifurcation structure
Keller–Miksis equation
ISSN:0924-090X, 1573-269X
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Zusammenfassung: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. During the simulations, the control parameters are the two amplitudes of the acoustic driving at fixed, commensurate frequency pairs. The high-resolution bi-parametric scans in the control parameter plane show that a period-2 attractor can be continuously transformed into a period-3 one (and vice versa) by proper selection of the frequency combination and by proper tuning of the driving amplitudes. This phenomenon has opened a new way to drive the system to a desired, pre-selected attractor directly via a non-feedback control technique without the need of the annihilation of other attractors. Moreover, the residence in transient chaotic regimes can also be avoided. The results are supplemented with simulations obtained by the boundary-value problem solver AUTO, which is capable to compute periodic orbits directly regardless of their stability, and trace them as a function of a control parameter with the pseudo-arclength continuation technique.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4358-z