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arXiv · 1209.3713

Systematic experimental exploration of bifurcations with non-invasive control

David A. W. Barton·Jan Sieber
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Abstract

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 non-invasive 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 non-invasive 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.

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David A. W. Barton, Jan Sieber. 2013-03-15. Systematic experimental exploration of bifurcations with non-invasive control. https://doi.org/10.1103/physreve.87.052916

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