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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Published in:Nonlinear dynamics Vol. 94; no. 1; pp. 273 - 293
Main Authors: Hegedűs, Ferenc, Lauterborn, Werner, Parlitz, Ulrich, Mettin, Robert
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.10.2018
Subjects:
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
Online Access:Get full text
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Abstract 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.
AbstractList 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.
Author Hegedűs, Ferenc
Mettin, Robert
Lauterborn, Werner
Parlitz, Ulrich
Author_xml – sequence: 1
  givenname: Ferenc
  surname: Hegedűs
  fullname: Hegedűs, Ferenc
  organization: Department of Hydrodynamic Systems, Faculty of Mechanical Engineering, Budapest University of Technology and Economics
– sequence: 2
  givenname: Werner
  surname: Lauterborn
  fullname: Lauterborn, Werner
  organization: Cavitation Bubble Dynamics Group, Drittes Physikalisches Institut, Georg-August-Universität Göttingen
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  givenname: Ulrich
  surname: Parlitz
  fullname: Parlitz, Ulrich
  email: ulrich.parlitz@ds.mpg.de
  organization: Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen
– sequence: 4
  givenname: Robert
  surname: Mettin
  fullname: Mettin, Robert
  organization: Cavitation Bubble Dynamics Group, Drittes Physikalisches Institut, Georg-August-Universität Göttingen
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Issue 1
Keywords Control of multistability
Nonlinear dynamics
Dual-frequency driving
GPU programming
Bifurcation structure
Keller–Miksis equation
Language English
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PublicationTitle Nonlinear dynamics
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Snippet A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller–Miksis equation...
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springer
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StartPage 273
SubjectTerms Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Original Paper
Vibration
Subtitle GPU accelerated topological analysis of a bubble in water
Title Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving
URI https://link.springer.com/article/10.1007/s11071-018-4358-z
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