Synchronization phenomena in coupled excitable systems

Synchronization phenomena are ubiquitous processes in nature. They
appear in systems as diverse as chemical reactions, peacemaker cells in
the heart, Josephson Junction arrays or populations of fireflies among
many other examples. In this context, phase models appear as minimal
systems that capture the essence of the phenomena and are amenable to
analytical study, and also as a reduced form of more complicated (and
realistic) systems.
In this work, we consider a system of non-identical globally coupled
active rotators near the excitable regimen. We show that the system
enters in a phase of synchronous firing as the diversity of the system
(dispersion of the distribution of natural frequencies) is increased.
This transition is found generically for any distribution with
well-defined moments. Singularly, the transition is not present for the
Lorentzian distribution (widely used in this context for its analytical
properties). This warns about the use of Lorentzian-type distributions
(and some recently proposed methods that rely on them) to understand the
generic properties of coupled oscillators.