Systematic experimental exploration of bifurcations with non-invasive control

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.

revised and extended version (8 pages, 7 figures)

References in corpus (3)

• Experimental continuation of periodic orbits through a fold
• An analytical limitation for time-delayed feedback control in autonomous systems
• A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

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