Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model
Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model
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DOI：
10.1007/s10955-015-1426-3
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发表时间：
2014-12
影响因子：
1.6
通讯作者：
D. Benedetto;E. Caglioti;Umberto Montemagno
中科院分区：
文献类型：
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作者：
D. Benedetto;E. Caglioti;Umberto Montemagno
研究了耦合常数低于同步阈值的耦合振子动力学Kuramoto模型。我们设法证明，对于任何解析的初始数据，如果相互作用是足够小的，模型的序参数指数快速消失，和解决方案是渐近描述的自由流。这种行为类似于等离子体物理中的朗道阻尼现象。在证明中，我们使用的技术组合从朗道阻尼和抽象的柯西Kowalewskaya定理。
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.