Landau damping in the Kuramoto model
The Kuramoto model is the archetype of heterogeneous systems of
(globally) coupled oscillators with dissipative dynamics. In this model,
the order parameter that quantifies the population synchrony decays to 0 in
time, as long as the interaction strength remains small (so that the
uniformly distributed stationary solution remains stable).
While this phenomenon has been identified since the first studies of the
model, its proof remained to be provided (most studies in the literature
are limited to the linearized dynamics).
The goal of this talk is to present rigorous results on the nonlinear
dynamics of the Kuramoto model, and in particular, a proof of damping of
the order parameter in the weak coupling regime. Time permitting, I'll talk
about proofs which closely follow recent approaches to Landau damping in
the Vlasov equation and in the Vlasov-HMF model.
Joint work with D. Gérard-Varet and G. Giacomin