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
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.