Systematic experimental exploration of bifurcations with noninvasive control

We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, ca...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2013-05, Vol.87 (5), p.052916-052916, Article 052916
Main Authors: Barton, D A W, Sieber, J
Format: Article
Language:English
Subjects:
Computer Simulation
Feedback
Models, Theoretical
Nonlinear Dynamics
Oscillometry - methods
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Summary:We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, can be overcome for tracking equilibria or forced periodic orbits in experiments. To demonstrate the use of our noninvasive control, we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.87.052916