H-theorem for a mean field model describing coupled oscillator systems under external forces

This article studies the asymptotic behavior of solutions of Fokker–Planck equations describing mean field approximations of weakly coupled oscillator systems subjected to external forces. Using an H-theorem we show that transient probability densities converge to stationary ones. Furthermore, stability criteria are derived for the stationary solutions of these Fokker–Planck equations. The obtained results are applied to a model that combines the Haken–Kelso–Bunz model and the models of weakly coupled oscillators proposed by Winfree and Kuramoto. The stability criteria based on the H-theorem agree with those derived in our earlier analyses.