Experimental continuation of periodic orbits through a fold

J Sieber; A Gonzalez-Buelga; SA Neild; DJ Wagg; B Krauskopf

Experimental continuation of periodic orbits through a fold

J Sieber, A Gonzalez-Buelga, SA Neild, DJ Wagg, B Krauskopf

Research output: Working paper

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Abstract

We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.

Original language	English
Publication status	Published - Apr 2008

Keywords

experimental bifurcation analysis
fold bifurcation
vertically forced pendulum

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http://hdl.handle.net/1983/1079

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Experimental continuation of periodic orbits through a fold
Sieber, J., Gonzalez Buelga, A., Neild, SA., Wagg, DJ. & Krauskopf, B., Jun 2008, In: Physical Review Letters. 100, 244101 , p. 1 - 4 4 p.
Research output: Contribution to journal › Article (Academic Journal) › peer-review
79 Citations (Scopus)

Cite this

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title = "Experimental continuation of periodic orbits through a fold",

abstract = "We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.",

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AU - Sieber, J

AU - Gonzalez-Buelga, A

AU - Neild, SA

AU - Wagg, DJ

AU - Krauskopf, B

PY - 2008/4

Y1 - 2008/4

N2 - We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.

AB - We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.

KW - experimental bifurcation analysis

KW - fold bifurcation

KW - vertically forced pendulum

M3 - Working paper

BT - Experimental continuation of periodic orbits through a fold

ER -

Experimental continuation of periodic orbits through a fold

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Research output

Experimental continuation of periodic orbits through a fold

Cite this