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DY: Dynamik und Statistische Physik
DY 30: Spiral Formation and Feedback
DY 30.4: Talk
Monday, March 7, 2005, 11:00–11:15, TU H3010
Delayed Feedback Control of Dynamical Systems at a Subcritical Hopf Bifurcation — •Klaus Höhne1, C. von Loewenich1, C.-U. Choe1, H. Benner1, W. Just2, K. Pyragas3, and V. Pyragas3 — 1Institut für Festkörperphysik TU-Darmstadt — 2Queen Mary, University of London, UK — 3Semiconductor Physics Institute, Vilnius, Lithuania
Delayed feedback control is a convenient tool to stabilize unstable periodic orbits embedded in strange attractors of chaotic systems. Here we consider the control of a torsion-free unstable periodic orbit originated in a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using a time averaging method. We discuss the necessity of employing an unstable degree of freedom in the feedback loop [1] as well as the effect of a nonlinear coupling between the controller and the controlled system. Our analytical approach is demonstrated for the specific example of a nonlinear electronic circuit [2]. Our analytical results are supported by both numerical simulations and real experiments. [1]K. Pyragas, Phys. Rev. Lett. 86, 2265 (2001). [2]K. Pyragas et al. Phys. Rev. E 70,026412 (2004).