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Longtime dynamics for interacting oscillators on graphs

publié le

Fabio Coppini
(Laboratoire de Probabilités, Statistique et modélisation, Université Paris Diderot)

This exposé focuses on a well-known 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 and homogeneous enough, then the behavior does not differ from the mean-field one. The emphasis will be put on the condition on the network, a convergence in the space of matrices or graphons, and on a stochastic partial differential equation, solved by the empirical measure of the system.