Abstract
Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game (MFG) version of the classical Kuramoto model, which describes synchronization phenomena in a large population of “rational” interacting oscillators. The MFG model exhibits several stationary equilibria, but the characterization of these equilibria and their ability to capture dynamic equilibria in long time remains largely open. In this paper, we demonstrate that, up to a phase translation, there are only two possible stationary equilibria: the incoherent equilibrium and the self-organizing equilibrium, given that the interaction parameter is sufficiently large. Furthermore, we present some local stability properties of the self-organizing equilibrium.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.