Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Pattern Formation / Reaction-Diffusion I

DY 24.2: Talk

Tuesday, March 21, 2017, 14:45–15:00, ZEU 147

Periodic sequence of stabilized wave segments in excitable media — •Vladimir Zykov and Eberhard Bodenschatz — Max-Planck-Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany

Wave segments represent an interesting and important example of spatio-temporal pattern formation in a broad class of nonlinear dynamic systems, so-called excitable media. They have been observed, for instance, in cardiac and cortex tissue, catalytic surface reactions, concentration waves in thin layers of the Belousov-Zhabotinsky reaction or during cell aggregation of Dictyostelium discoideum. For a given excitability a medium supports propagation of a wave segment with a selected size and shape, which is intrinsically unstable. In order to make this solution observable it has to be stabilized by an adequate noninvasive feedback control. For the case of a solitary propagating wave segments a universal selection rules have been found by use a free-boundary approach. The main aim of our study is to generalize these results on a case of a periodic sequence of wave segments. To this aim the translational motion of a stabilized wave segment in an excitable medium is numerically studied by use of a generic reaction-diffusion model with nonlinear activator-inhibitor kinetic. In addition, the free-boundary approach is applied to determine the wave segment shape and the speed as functions of the medium parameters. We hope that the results obtained in this study are also applicable to the spiral wave dynamics.