H-theorem for a mean field describing coupled oscillators under external forces

T.D. Frank, A. Daffertshofer, C.E. Peper, P.J. Beek, H. Haken

    Research output: Contribution to JournalArticleAcademicpeer-review


    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.
    Original languageEnglish
    Pages (from-to)219-236
    JournalPhysica D. Nonlinear Phenomena
    Publication statusPublished - 2001


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