Long time dynamics for interacting oscillators on graphs

schedule le lundi 18 novembre 2019 de 17h00 à 18h00

Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu

Intervenant : Fabio Coppini (LPSM)
Lieu : P6 Jussieu 16-26-209

Sujet : Long time dynamics for interacting oscillators on graphs

Résumé :
Abstract: This exposé will focus on a famous system of interacting oscillators, 
the Kuramoto model, and the relationship between its long time behavior 
and the structure of the underlying network of connections. The 
classical model is of mean-field type, where each unit interacts with 
all the others in exactly the same way; we will consider a 
generalization allowing each particle to communicate with only a portion 
of the others, showing that, if this portion is big enough, then the 
behavior remains unchanged. The model, admitting a phase transition 
depending on the coupling strength, will be studied in all regimes and 
emphasis will be put both on the condition on the network, a convergence 
in the space of matrices or graphons, and on a mild stochastic partial 
differential equation, solved by the empirical measure of the 

interacting units.