Dephasing of Kuramoto oscillators in kinetic regime towards a fixed asymptotically free state

2014/11/23 by Dario Benedetto, Benedetto, Dario, Emanuele Caglioti +3
Mathematics · Physics and Astronomy · #74A25 #76N10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:74A25 #msc:76N10

paper · pdf · doi:10.48550/arxiv.1411.6304

arxiv created 2014/11/23 · arxiv updated 2014/11/25

Abstract

We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular asymptotically free state, if the interaction is small enough, it exists a solution which is asymptotically close to it. For this class of solution the order parameter vanishes to zero, showing a behavior similar to the phenomenon of Landau damping in plasma physics. We obtain an exponential decay of the order parameter in the case on analytical regularity of the asymptotic state, and a polynomial decay in the case of Sobolev regularity.

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