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2008•Physical Review LettersOpen access

Experimental Continuation of Periodic Orbits through a Fold

Jan Sieber, Alicia Gonzalez-Buelga, Simon A. Neild, David Wagg, Bernd Krauskopf

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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.

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What this paper is about

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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Available 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.

Key concepts: Continuation, Periodic orbits, Bifurcation, Numerical continuation, Fold (higher-order function), Physics, Pendulum, Orbit (dynamics)

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