Stability and Synchrony in the Kuramoto Model -
We will discuss the notion of stability of a fixed point of a dynamical system generally, with particular attention to gradient flows and particularly the Kuramoto model, a model for the synchronization of coupled oscillators. In particular we will discuss the case where the natural frequencies are randomly distributed. In the proper scaling we’ll show that there is a phase transition — for weak couplings the probability that the oscillators synchronize is identically zero, while above a certain cutoff synchronization happens with probability one. This talk will be accessible to anyone with calculus and a bit of linear algebra under their belt.