Séminaire OrléansPhénomènes macroscopiques pour une dynamique d'oscillateurs couplés inspirée d'expériences de populations de circuits génétiques synthétiques
Bastien Fernandez (Marseille/Paris 7)
Thursday 20 March 2014 14:00 - Orléans - Salle de Séminaire
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.