Transition to Massive Clustering in Populations of Degrade-and-fire Oscillators

Wednesday, May 15, 2013 - 11:30am - 12:20pm
Keller 3-180
Bastien Fernandez (Centre National de la Recherche Scientifique (CNRS))
In this talk, I will present rigorous results on the dynamics of a piecewise affine system of pulse-coupled oscillators with global interaction, inspired by experiments on synchronization in colonies of bacteria-embedded genetic circuits.
Due to global coupling, any cluster composed by a group of oscillators in sync is invariant in time. Hence the analysis essentially boils down to estimating possible asymptotic cluster distributions depending on the initial conditions.
I will show that, as the coupling strength increases, the system exhibits a sharp transition between a regime of arbitrary asymptotic distributions, to a strongly clustered regime where every surviving distribution must contain a giant cluster.
I will also 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 asymptotic clusters remains bounded in the thermodynamic limit, while the maximum number linearly diverges.
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