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Journal of Statistical Physics

, Volume 162, Issue 4, pp 813–823 | Cite as

Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model

  • Dario Benedetto
  • Emanuele CagliotiEmail author
  • Umberto Montemagno
Article

Abstract

We study the kinetic Kuramoto model for coupled oscillators with coupling constant below the synchronization threshold. We manage to prove that, for any analytic initial datum, if the interaction is small enough, the order parameter of the model vanishes exponentially fast, and the solution is asymptotically described by a free flow. This behavior is similar to the phenomenon of Landau damping in plasma physics. In the proof we use a combination of techniques from Landau damping and from abstract Cauchy–Kowalewskaya theorem.

Keywords

Kuramoto model Dephasing Landau damping Abstract Cauchy–Kowalewskaya theorem 

Mathematics Subject Classification

35A10 35Q92 74A25 76N10 92B25 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Dario Benedetto
    • 1
  • Emanuele Caglioti
    • 1
    Email author
  • Umberto Montemagno
    • 1
  1. 1.Dipartimento di MatematicaSapienza Università di RomaRomeItaly

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