H-theorem for a mean field describing coupled oscillators 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.