Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 36: Nonlinear Dynamics, Synchronization and Chaos II

DY 36.3: Talk

Wednesday, March 29, 2006, 16:45–17:00, H\"UL 186

Robust control of torsionfree unstable periodic orbits — •Klaus Höhne¹, Chol-Ung Choe^1,2, Hiroyuki Shirahama^1,3, Hartmut Benner¹, and Kestutis Pyragas⁴ — ¹Institut für Festkörperphysik, TU Darmstadt, Germany — ²Department of Physics, University of Science, Pyongyang, DPR Korea — ³Ehime University, Matsuyama, Japan — ⁴Semiconductor Physics Institute, Vilnius, Lithuania

Torsionfree unstable periodic orbits cannot be stabilized by conventional time-delayed feedback control. The most simple example of such an orbit occurs at a subcritical Hopf bifurcation. Analytical and numerical investigations showed successful control of a torsionfree unstable periodic orbit in an unstable van der Pol oscillator by applying the idea of a nonlinear unstable time-delayed feedback controller [1].

We succeeded to stabilize a torsionfree unstable periodic orbit in experiment by an electronic circuit realization of this model. The experiment pointed out that the basin of attraction of the controlled orbit is very small, so that the practical application of this method might be difficult. In order to achieve robust control of such an orbit we modified the nonlinear coupling of the unstable time-delayed feedback control. We discuss the advantages of this method in comparison with the original idea.

[1] K. Pyragas et al., Phys. Rev. E 70, 026412