Münster 1997 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Nichtlineare Dynamik und Chaos I

DY 21.2: Talk

Thursday, March 20, 1997, 15:45–16:00, R4

On the Mechanism of Time–Delayed Feedback Control — •Wolfram Just, Ekkehard Reibold, and Hartmut Benner — Institut für Festkörperphysik, Technische Hochschule Darmstadt, Hochschulstraße 8, 64289 Darmstadt, and SFB 185

The Pyragas method for controlling chaos does not require any phase space reconstruction of the dynamics. For that reason the method is easily applied to real experimental situations and has become quite popular. But a sound theoretical understanding of the control method still seems to be lacking. By performing an analytical linear stability analysis we show that the revolution around the unstable periodic orbit governs the success of the controlling scheme. We derive expressions for the critical and optimal control amplitude and obtain the dependence of the transient behaviour on the control parameters. Our analytical predictions are in agreement with experimental data.