Systematic experimental exploration of bifurcations with noninvasive control
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
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.
Engineering and Physical Sciences Research Council (EPSRC)
Copyright © 2013 American Physical Society
Vol. 87 (5), article 052916