Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Cardiac dynamics and reaction-diffusion systems

DY 13.1: Talk

Tuesday, February 26, 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.