title: Emergence of Asynchronous Local Clocks in Excitable Media.
abstract: 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 mechanism can occur in a wide range of excitable media.
authors.affiliation: Department of Physics, University of Erlangen-Nuremberg, Erlangen, Germany.
authors.forename: Richard Carl
authors.initials: RC
authors.lastname: Gerum
authors.affiliation: Department of Physics, University of Erlangen-Nuremberg, Erlangen, Germany.
authors.forename: Ben
authors.initials: B
authors.lastname: Fabry
authors.affiliation: Department of Physics, University of Erlangen-Nuremberg, Erlangen, Germany.
authors.forename: Claus
authors.initials: C
authors.lastname: Metzner
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D001921:Brain / Q000502:physiology; D006321:Heart / Q000502:physiology; D006801:Humans; D008962:Models, Theoretical