Tracking nonlinear oscillations with time-delayed feedback

J. Sieber; B Krauskopf

Tracking nonlinear oscillations with time-delayed feedback

J. Sieber, B Krauskopf

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

Abstract

We demonstrate a method for tracking the onset of nonlinear oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable. We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.

Translated title of the contribution	Tracking nonlinear oscillations with time-delayed feedback
Original language	English
Title of host publication	6th International Conference on Modern Practice in Stress and Vibration Analysis 2006
Publication status	Published - Apr 2006

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Name and Venue of Event: Bath, United Kingdom
Other: http://www.scientific.net/

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http://rose.bris.ac.uk/dspace/handle/1983/496

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Tracking nonlinear oscillations with time-delayed feedback
Sieber, J. & Krauskopf, B., 10 Apr 2006.
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@inproceedings{e89efafd7d6c448b971d52951ec1273d,

title = "Tracking nonlinear oscillations with time-delayed feedback",

abstract = "We demonstrate a method for tracking the onset of nonlinear oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable. We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.",

author = "J. Sieber and B Krauskopf",

note = "Name and Venue of Event: Bath, United Kingdom Other: http://www.scientific.net/",

year = "2006",

month = apr,

language = "English",

booktitle = "6th International Conference on Modern Practice in Stress and Vibration Analysis 2006",

}

TY - GEN

T1 - Tracking nonlinear oscillations with time-delayed feedback

AU - Sieber, J.

AU - Krauskopf, B

N1 - Name and Venue of Event: Bath, United Kingdom Other: http://www.scientific.net/

PY - 2006/4

Y1 - 2006/4

N2 - We demonstrate a method for tracking the onset of nonlinear oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable. We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.

AB - We demonstrate a method for tracking the onset of nonlinear oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable. We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.

M3 - Conference Contribution (Conference Proceeding)

BT - 6th International Conference on Modern Practice in Stress and Vibration Analysis 2006

ER -

Tracking nonlinear oscillations with time-delayed feedback

Abstract

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Tracking nonlinear oscillations with time-delayed feedback

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