Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 13: Cardiac dynamics and reaction-diffusion systems
DY 13.1: Vortrag
Dienstag, 26. Februar 2008, 11:30–11:45, MA 004
Different forms of alternans in the modified Beeler-Reuter model for cardiac dynamics and chaotic media — Georg Röder1, Blas Echebarria2, Jörn Davidsen3, Steffen Bauer4, and •Markus Bär4 — 1MPIPKS Dresden — 2UPC Barcelona, Spain — 3University of Calgary, Canada — 4PTB Berlin
We investigate the phenomena of spatial period doubling and alternans of by numerical simulations and stability analysis of one-dimensional coherent structures in reaction-diffusion models. In general, the onset of alternans in different media can be related to a linear instability of periodic waves that is either a period doubling or a Hopf bifurcation. In chaotic media a period doubling of wavetrains is found, while in the modified Beeler-Reuter model of cardiac tissue period doubled wave trains stemming from a non-monotonous dispersion curve as well as Hopf bifurcations leading to temporary modulations of wave trains are observed. Period doubling bifurcations of wavetrains are related to real eigenvalues and lead to alternant wavetrains, whereas Hopf bifurcations correspond to purely imaginary eigenvalues displaying a frequency that is roughly half of the temporal frequency of the original wave train and produce . Implications for structures in higher dimensions are briefly discussed.