Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Reaction-diffusion systems
DY 17.1: Talk
Wednesday, March 25, 2009, 14:45–15:00, ZEU 118
Controlling the onset of traveling pulses in reactions-diffusion systems by nonlocal feedback — •MarkusA. Dahlem1, Felix M. Schneider1, Jens Dreier2, and Eckehard Schöll1 — 1Institut für Theoretische Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany — 2Klinik für Neurologie, Charite, Universitätsmedizin Berlin
The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by nonlocal spatial coupling and by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations while nonlocal feedback changes excitability. For certain ranges of RD and feedback parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change of RD parameters that can be expressed by algebraic functions of the control gain factor as the major control parameter. A distinctly new character is, however, added to the RD patterns outside these ranges. New patterns are obtained, for example step-wise propagation due to delay-induced oscillations. Nonlocal feedback constitutes a complementary signalling system to the classical RD mechanism of pattern formation. As a hybrid model, it combines the two major signalling systems in the brain, namely volume transmission and synaptic transmission. This theoretical model is developed in conjunction with experiments on the transition between RD pulse patterns and epileptic activity at an anatomical border.