Systematic experimental exploration of bifurcations with noninvasive control

D. A. W. Barton*, J. Sieber

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

23 Citations (Scopus)

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 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.

Original languageEnglish
Article number052916
Number of pages7
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number5
DOIs
Publication statusPublished - 28 May 2013

Keywords

  • DELAYED FEEDBACK-CONTROL
  • PERIODIC-ORBITS
  • CHAOS

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