title: Onset of time dependence in ensembles of excitable elements with global repulsive coupling.
abstract: We consider the effect of global repulsive coupling on an ensemble of identical excitable elements. An increase of the coupling strength destabilizes the synchronous equilibrium and replaces it with many attracting oscillatory states, created in the transcritical heteroclinic bifurcation. The period of oscillations is inversely proportional to the distance from the critical parameter value. If the elements interact with the global field via the first Fourier harmonics of their phases, the stable equilibrium is in one step replaced by the attracting continuum of periodic motions.
authors.affiliation: Institute of Physics and Astronomy, Potsdam University, 14465 Potsdam, Germany.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Zaks
authors.affiliation: Institute of Physics, Humboldt University at Berlin, 12489 Berlin, Germany.
authors.forename: Petar
authors.initials: P
authors.lastname: Tomov