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Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model.

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Title: Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model.
Authors: Benedetto, Dario1, Caglioti, Emanuele1, Montemagno, Umberto1
Source: Journal of Statistical Physics. Feb2016, Vol. 162 Issue 4, p813-823. 11p.
Subjects: Nonlinear oscillators, Cauchy transform, Oscillation theory of difference equations, Landau damping, Synchronization
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model.
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10955-015-1426-3
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      – SubjectFull: Cauchy transform
        Type: general
      – SubjectFull: Oscillation theory of difference equations
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      – SubjectFull: Landau damping
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      – SubjectFull: Synchronization
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      – TitleFull: Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model.
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