Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Time-delayed feedback and neural networks

DY 7.6: Vortrag

Montag, 25. Februar 2008, 17:45–18:00, A 053

Delay sustained pattern formation in subexcitable media — •Martin Gassel, Erik Glatt, and Friedemann Kaiser — Institute of Applied Physics, TU Darmstadt, Germany

In the last decades a lot of investigations on the dynamics of nonlinear systems and their control have been done. Many of them focus on time-delayed feedback control, a widely used method to achieve a qualitative change in the system dynamics. Pyragas introduced a feedback control scheme to stabilize an unstable orbit of a chaotic attractor to control deterministic chaos. In other investigations time-delayed feedback is used to control the coherence of noise-induced oscillations or to suppress limit cycle oscillations (amplitude death). In the present contribution the influence of time-delayed feedback on pattern formation in subexcitable media represented by a net of FitzHugh-Nagumo elements is studied. Without feedback wave fronts, which are either induced by special initial conditions or by additive noise, die out after a short propagation length (subexcitable net dynamics). Applying time-delayed feedback with appropriate feedback parameters pattern formation is sustained and the wave fronts may propagate through the whole net. The coherence of the patterns and the life time of the wave fronts are investigated dependent on the feedback strength and the delay time. It is shown that both the coherence of the patterns and the life time of the wave fronts are significantly larger, if feedback with appropriate parameters is applied.