Synchronization in a Kuramoto mean field game

Rene Carmona, Quentin Cormier, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is demonstrated by the stability of the uniform distribution. Above this value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions get stronger, these stationary solutions become fully synchronized. Results are proved by an amalgam of techniques from nonlinear partial differential equations, viscosity solutions, stochastic optimal control and stochastic processes.

Original languageEnglish (US)
Pages (from-to)1214-1244
Number of pages31
JournalCommunications in Partial Differential Equations
Issue number9
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Kuramoto model
  • Mean field games
  • synchronization
  • viscosity solutions


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