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 tran sient probability densities converge to stationary ones. Furthermore, stabi lity criteria are derived for the stationary solutions of these Fokker-Plan ck equations. The obtained results are applied to a model that combines the Haken-Kelso-Bunz model and the models of weakly coupled oscillators propos ed by Winfree and Kuramoto. The stability criteria based on the H-theorem a gree with those derived in our earlier analyses. (C) 2001 Elsevier Science B.V. All rights reserved.