 |
Center for Nonlinear Studies |
The spontaneous synchronization of oscillators interacting via a weak coupling has been known and observed since a long time and in a lot of different physical situations. In 1975 Y. Kuramoto introduced a simple model able to describe such populations. This model has been widely studied since, from the most fundamental point of view to its many possible applications. Yet, its non standard bifurcations still present many theoretical challenges.In this seminar I will present the basic model and expose the classical results about the bifurcations toward synchronization when the coupling is increased. I will then show how any small inertia can completely change the bifurcation diagram, due to new singularities. I will put these results into perspective with the Vlasov equation - describing for example plasma and self-gravitating systems - which features similar non standard bifurcations.
Host: Michael Chertkov