The Kuramoto Mean Field Game

par Dr Quentin Cormier

mardi 30 sept. 2025, 14:00 → 15:00 Europe/Paris

The classical Kuramoto model (1975) describes a collection of coupled oscillators, each with its own intrinsic frequency, and studies how these oscillators synchronize their phases under the influence of their interactions. We study a variant of this model formulated as a mean field game type with infinite horizon.

Our analysis shows that when the interaction parameter is below an explicit critical value, the system remains incoherent, with the uniform distribution as a stable solution. Once this threshold is crossed, a bifurcation occurs and self-organizing solutions, either stationary or time-periodic, emerge.

I will explain our approach for the stability analysis in the subcritical regime and present some open questions.

This is joint work with René Carmona and Mete Soner.