Münster 1999 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 13: Niedrigdimensionales Chaos
DY 13.1: Vortrag
Montag, 22. März 1999, 11:00–11:15, R1
Limits of time–delayed feedback control methods — •E. Reibold1, H. Benner1, W. Just2, and J. Hołyst3 — 1Institut für Festkörperphysik, TU Darmstadt — 2Max Planck Institut für Physik komplexer Systeme, Dresden — 3Institute of Physics, Warsaw University of Technology, Poland
Time–delayed feedback schemes have been designed to control periodic motions in particular in ultrafast experimental situations. Meanwhile, several features of this approach are quite well understood (cf. [1] for recent reviews). Unfortunately there does not exist any general knowledge about control domains, i. e. regions in parameter space where stabilisation is possible. Numerical analysis of particular model systems indicate that unstable orbits with long periods or large Lyapunov exponents are difficult to stabilise with the original Pyragas method, whereas more advanced schemes involving multiple delay terms seem to overcome such a limitation [2]. Here we attack this problem from a systematic point of view. An approximate treatment of the linear stability analysis gives estimates for the control domains as well as the critical Lyapunov exponents. We demonstrate that multiple delay schemes indeed improve the simple time–delayed feedback method considerably. Our findings are consistent with experimental data from electronic circuit experiments.
[1] Handbook of Chaos Control, Ed. H. G. Schuster, (Wiley-VCH, 1998)
[2] J. E. S. Socolar, D. W. Sukov, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994)