Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Poster II

DY 26.18: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1A

Hysteresis in pinning and depinning of spiral waves — Vladimir Zykov¹, Grigory Bordyugov², Hartmut Lentz¹, and •Harald Engel¹ — ¹Institut für Theoretische Physik, TU Berlin, D-10623 Berlin, Germany — ²Institut für Physik und Astronomie, Universität Potsdam, D-14476 Potsdam, Germany

For the FitzHugh-Nagumo model hysteresis in the transition between pinning and depinning of spiral waves rotating around a hole in a two-dimensional excitable medium has been studied both by use of the continuation software AUTO and by direct numerical integration of the reaction-diffusion equations. To clarify the role of curvature and dispersion in this phenomenon, a kinematical description is applied. It assumes the existence of a boundary layer of finite thickness ahead of the wave front and results in a nonlinear velocity-curvature relationship (eikonal equation) for the front velocity. It is found that the hysteresis phenomenon can be reproduced qualitatively in the framework of the boundary layer model even when dispersion is neglected. However, to obtain a quantitative agreement with results obtained from the reaction-diffusion model, both the nonlinear eikonal equation and the dispersion relation have to be taken into account.