Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Cardiac dynamics and reaction-diffusion systems

DY 13.5: Vortrag

Dienstag, 26. Februar 2008, 12:30–12:45, MA 004

Hysteresis in the selection of rotating wave patterns — •Hartmut Lentz, Vladimir Zykov, and Harald Engel — Institut für Theoretische Physik, TU Berlin, Hardenbergstr. 36, D-10623 BERLIN

We study rotating wave patterns in an annular channel as spiral waves, rotating wave segments and boundary spots. Usually, a unique rotation period and wave shape are selected for given channel geometry and parameters of the medium. Within a modified kinematic approach that takes into account a boundary layer in the wave front, we derive a nonlinear eikonal equation with an unstable branch. Based on this equation we describe the transformation of rotating segments pinned to the inner boundary into a freely rotating spiral wave. Additionally, we specify a regime with hysteresis of the rotation frequency under variation of the inner radius. We conclude, that dispersion effects are not the crucial factor for the hysteresis in the rotation period. The theoretical predictions are compared with results obtained by numerical simulation of the underlying reaction-diffusion equations.

[1] G. Bordyugov and H. Engel: Continuation of spiral waves. 2007.

[2] A. Pertsov et. al.: Rotating spiral waves in a modified fitzhugh-nagumo-model, 1984.

[3] V. Zykov: Selection mechanism for rotating patterns in weakly excitable media, 2007.