title: Theory of collective firing induced by noise or diversity in excitable media.
abstract: Large variety of physical, chemical, and biological systems show excitable behavior, characterized by a nonlinear response under external perturbations: only perturbations exceeding a threshold induce a full system response (firing). It has been reported that in coupled excitable identical systems noise may induce the simultaneous firing of a macroscopic fraction of units. However, a comprehensive understanding of the role of noise and that of natural diversity present in realistic systems is still lacking. Here we develop a theory for the emergence of collective firings in nonidentical excitable systems subject to noise. Three different dynamical regimes arise: subthreshold motion, where all elements remain confined near the fixed point; coherent pulsations, where a macroscopic fraction fire simultaneously; and incoherent pulsations, where units fire in a disordered fashion. We also show that the mechanism for collective firing is generic: it arises from degradation of entrainment originated either by noise or by diversity.
authors.affiliation: Institut Mediterrani d'Estudis Avançats, IMEDEA (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
authors.forename: C J
authors.initials: CJ
authors.lastname: Tessone
authors.forename: A
authors.initials: A
authors.lastname: Scirè
authors.forename: R
authors.initials: R
authors.lastname: Toral
authors.forename: P
authors.initials: P
authors.lastname: Colet