Steven Strogatz: Global Synchronization: New Theorems, New Puzzles

Title: New Theorems, New Puzzles

Abstract: Consider a network of N identical Kuramoto oscillators. Suppose all the coupling strengths are equal and bidirectional, and each oscillator is connected to at least 𝜇(N-1) other oscillators, where 0 ≤ 𝜇 ≤ 1. How likely is the network to end up in perfect synchrony, starting from random initial conditions? It's known that all networks with sufficiently large 𝜇 will globally synchronize, but how large is large enough? In this Zoom talk, I'll discuss the big gap - and the big unsolved puzzle about what happens - between the best known upper and lower bounds on the critical connectivity 𝜇c above which all such networks globally synchronize. I'll also mention what is currently known for randomly connected networks. This is joint work with Alex Townsend, Mike Stillman, and Martin Kassabov.