20-22 mars 2017 Autrans (France)
Landau damping in the Kuramoto model
Helge Dietert  1@  
1 : Institut de Mathématiques de Jussieu - Paris Rive Gauche  (IMJ-PRG)  -  Site web
Université Paris Diderot - Paris 7
Université Paris Diderot, UFR de Mathématiques Bâtiment Sophie Germain, Bureau 724 75205 Paris Cedex 13 -  France

The Kuramoto model is a kinetic model of oscillators for studying synchronisation behaviours. Like the Vlasov-Poisson equation it has a stability mechanism through phase mixing in weak topologies, which is the Landau damping. Compared to the Vlasov-Poisson equation, the interaction in the Kuramoto model is simpler allowing more results. In particular, we can study the stability of spatially inhomogeneous states.

In this talk, I will introduce (i) the Kuramoto model, (ii) the Landau damping and (iii) the stability of inhomogeneous states.

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