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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 8: Poster

SOE 8.17: Poster

Montag, 16. März 2015, 18:00–20:00, Poster E

Emergence of asynchronous local clocks in excitable media — Richard Gerum, •Achim Schilling, Ben Fabry, and Claus Metzner — Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg (FAU), Germany

Excitable media such as the myocardium or the brain consist of arrays of coupled excitable elements, in which the local excitation of a single element can propagate to its neighbors in the form of a non-linear autowave. Since each element has to pass through a refractory period immediately after excitation, the frequency of autowaves is self-limiting. In this work, we consider the case where each element is spontaneously excited at a fixed average rate and thereby initiates a new autowave. Although these spontaneous self-excitation events are modelled as independent Poisson point processes with exponentially distributed waiting times, the travelling autowaves lead collectively to a non-exponential, unimodal waiting time distribution for the individual elements. With increasing system size, a global ’clock’ period T emerges as the most probable waiting time for each element, which fluctuates around T with an increasingly small but non-zero variance. This apparent synchronization between asynchronous, temporally uncorrelated point processes differs from synchronization effects between perfect oscillators interacting in a phase-aligning manner. Finally, we demonstrate that asynchronous local clocks also emerge in non-homogeneous systems in which the rates of self-excitation are different for all individuals, suggesting that this novel synchronization mechanism can occur in a wide range of excitable media.