Extensive clustering in populations of degrade-and-fire oscillators
In this talk, I will present (additional) results on the
piecewise affine system of pulse-coupled oscillators with global
interaction, inspired by recent experiments on synchronization in colonies
of bacteria-embedded genetic circuits.
In a previous talk, I showed the existence of a phase transition with the
coupling strength, from a regime of arbitrary asymptotic cluster sizes, to
a strongly clustered regime where every asymptotic distribution contains
an extensive cluster. I also presented an expression for the maximal
number of asymptotic clusters and showed that, while it decreases in the
strong coupling regime, this number stays extensive for every coupling
Here, I will report on manifestations of this phase transition in the
dynamics of uniformly drawn random initial conditions. The most
significant feature is that, when the coupling strength is sufficiently
large, with positive probability, the number of clusters remains intensive
in the thermodynamic limit.