Random natural frequencies, active dynamics and coherence stability in populations of coupled rotators

Random natural frequencies, active dynamics and coherence stability in populations of coupled rotators

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Giambattista Giacomin, Université Paris Diderot
Jadwin Hall A06

The Kuramoto synchronization model is the reference model for synchronization phenomena in biology (and, to a certain extent, also in other fields). The model is formulated as a dynamical system of interacting plane rotators. Variations of it provide basic models of phenomena beyond synchronization, such as noise induced coherent oscillations. The talk will focus on the case on noisy dynamics, with different rotators stirred by independent Brownian motions. The approach we present is based on the observation that in the absence of disorder the Kuramoto model reduces to a Langevin dynamics for the mean field plane rotator (or classical XY spin) model. The analysis is carried at the level of the Fokker-Planck PDE for the evolution of the system's empirical density, in the limit where N tends to infinity.