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DY: Dynamik und Statistische Physik
DY 40: Nonlinear dynamics III
DY 40.5: Talk
Thursday, March 27, 2003, 10:45–11:00, G\"OR/226
Do stable Floquet exponents influence time-delayed feedback control? — •Hartmut Benner1, Ekkehard Reibold1, Krzysztof Kacperski2, Piotr Fronczak2, Janusz A. Holyst2, and Wolfram Just3 — 1Institut für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt — 2Faculty of Physics, Warsaw University of Technology,PL-00-662 Warsaw — 3Institut für Physik, TU Chemnitz, D-09107 Chemnitz
The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that also eigenbranches which develop from the stable Lyapunov exponents of the free system have a strong influence on the control properties, either by hybridisation or by a crossing of branches which interchange the role of the leading eigenvalue. Our findings are confirmed by numerical analysis of two particular examples, the Toda and the Rössler model. More important is the verification by actual electronic circuit experiments. Here, the observed reduction of control domains can be attributed to these additional eigenvalue branches. The investigations lead to a thorough analytical understanding of the stability properties in time-delayed feedback systems.