# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 36: Nonlinear Dynamics, Synchronization and Chaos II

### DY 36.6: Vortrag

### Mittwoch, 29. März 2006, 17:30–17:45, H\"UL 186

**Time-delayed feedback control with variable phase-dependent coupling** — •Philipp Hövel^{1}, Eckehard Schöll^{1}, and Hans-Jürgen Wünsche^{2} — ^{1}Technische Universität Berlin, 10623 Berlin, Germany — ^{2}Humboldt-Universität zu Berlin, 12489 Berlin, Germany

During the last decade time-delayed feedback methods have been successfully used to control unstable periodic orbits as well as unstable steady states[1]. In most of the theoretical analysis, this control method is considered in the realization of diagonal coupling, i.e., the control force applied to the i-th component of the system is a function of exclusively the same component. Although diagonal coupling is suitable for a theoretical investigation, it is often not feasible for an experiment. Therefore we consider the more general case where control is effected by a nondiagonal coupling matrix. Specifically, we investigate the time-delayed feedback scheme for a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and show the application to optical systems [2] where the optical phase is an additional degree of freedom.

[1] P. Hövel and E. Schöll, Phys. Rev. E **72**, 046203 (2005)

[2] V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, submitted to Phys. Rev. E (2005)