Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Poster I
DY 17.49: Poster
Dienstag, 26. Februar 2008, 16:00–18:00, Poster C
Conversion of Stability in Systems close to a Hopf Bifurcation by Time-delayed Coupling — Chol-ung Choe1,2, Valentin Flunkert2, •Philipp Hövel2, Hartmut Benner3, and Eckehard Schöll2 — 1Department of Physics, University of Science, Unjong-District, Pyongyang, DPR Korea — 2Institut f. Theo. Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany — 3Institut für Festkörperphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
We propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a Hopf bifurcation. We consider two delay-coupled normal forms for Hopf bifurcation and demonstrate the conversion of stability, i.e., an interchange between the sub- and supercritical Hopf bifurcation. [1] The control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking. The main method and the results are applicable to a wide class of systems showing Hopf bifurcations, for example, the Van der Pol oscillator. The analytical theory is supported by numerical simulations of two delay-coupled Van der Pol oscillators, which show good agreement with the theory.
[1] C.-U. Choe et al., Phys. Rev. E 75, 046206 (2007).