Dresden 2006 – wissenschaftliches Programm

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SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

SYSS 1: Structure Formation and Self-Organization in non-equilibrium Systems I

SYSS 1.11: Vortrag

Donnerstag, 30. März 2006, 12:15–12:30, BAR Sch\"o

Pulse propagation in excitable media at the edge to oscillatory kinetics. — •Grigori Bordiougov, Georg Roeder, and Harald Engel — Institut fuer Theoretische Physik, TU Berlin, Hardenbergstr. 36 10623 Berlin

Small amplitude oscillations in the wake of solitary pulses are shown to have a strong impact on the interaction between excitation pulses. Annihilation of colliding pulses is replaced by reflective collision. In addition to this soliton-like behavior we find bistability in the dispersion curve for periodic pulse trains [1]. Close to the Canard explosion in the local dynamics we observe break-up of the dispersion curve into disconnected branches accompanied by the formation of isolas [2]. Our results shed new light on the still open mechanism of the transition between trigger and phase waves in reaction-diffusion systems [3]. The reported behavior is generic for a whole class of media with an unique homogeneous steady state that undergoes a supercritical Hopf-bifurcation with Canard explosion due to well separated time scales (so-called type II excitable systems [4]).

1. G. Bordiougov et al., Phys. Rev. Lett. 90(14), 148302 (2003).

2. G. Roeder et al., Bistable dispersion relation in an excitable FitzHugh-Nagumo model, in preparation.

3. G. Bordiougov et al., From Trigger to Phase Waves and Back Again, submitted to Physica D.

4. E. Izhikevich, Int. J. of Bif. and Chaos 10 1171-1266 (2000).

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