Landau damping in the Kuramoto model

Abstract : We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit, with individual frequencies drawn from a distribution with density of class Cn (n≥4). A criterion for linear stability of the uniform stationary state is established which, for basic examples of frequency distributions, is equivalent to the standard condition on the coupling strength in the literature. We prove that, under this criterion, the Kuramoto order parameter, when evolved under the full nonlinear dynamics, asymptotically vanishes (with polynomial rate n) for every trajectory issued from sufficiently small Cn perturbation. The proof uses techniques from the Analysis of PDEs and closely follows recent proofs of the nonlinear Landau damping in the Vlasov equation and Vlasov-HMF model.
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Article dans une revue
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2016, 17 (7), pp.1793-1823
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Contributeur : Philippe Macé <>
Soumis le : jeudi 16 mars 2017 - 10:50:56
Dernière modification le : samedi 18 mars 2017 - 01:10:55

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  • HAL Id : hal-01490933, version 1

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Bastien Fernandez, David Gérard-Varet, Giambattista Giacomin. Landau damping in the Kuramoto model. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2016, 17 (7), pp.1793-1823. <hal-01490933>

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