Research seminar on complex systems. Speaker: Artem Alexandrov (MIPT, Russia)
Basics of Kuramoto model
We examine essential facts about Kuramoto model. We start from the brief discussion of Hopf bifurcation and Landau-Stuart oscillators. We mostly focus on the model with all-to-all couplings and consider continuum limit of the Kuramoto model. We discuss the integrability in the Kuramoto model and Ott-Antonsen ansatz. Next, we extend our discussion to the Kuramoto-Sakaguchi model. Then, we consider the Kuramoto model on star graph and discuss its features. In the end of our narration, we present some quite fresh ideas about the Kuramoto model and speculate about their perspectives.