Kuramoto模型中的瞬时频率
Instantaneous frequencies in the Kuramoto model
摘要：
使用的主要结果的仓本理论的全球耦合相位振荡器结合的方法，从概率和广义函数理论的几何分析，我们扩展仓本的结果，并获得一个数学描述的瞬时频率（相速度）分布。我们的结果进行了验证，对数值模拟，我们说明它的情况下，固有频率有正常和Beta分布。在这两种情况下，我们不同的耦合强度和比较系统的时间平均频率的分布（一个已知的结果仓本理论）的瞬时频率，集中在他们的定性差异附近的同步频率，并在他们的尾巴。对于一类具有幂律尾的固有频率分布，其中包括柯西-洛伦兹分布，我们通过对瞬时频率分布进行幂级数展开得到的渐近公式来分析罕见事件。
英文摘要：
Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical description of the instantaneous frequency (phase-velocity) distribution. Our result is validated against numerical simulations, and we illustrate it in cases where the natural frequencies have normal and Beta distributions. In both cases, we vary the coupling strength and compare systematically the distribution of time-averaged frequencies (a known result of Kuramoto theory) to that of instantaneous frequencies, focussing on their qualitative differences near the synchronized frequency and in their tails. For a class of natural frequency distributions with power-law tails, which includes the Cauchy-Lorentz distribution, we analyze rare events by means of an asymptotic formula obtained from a power series expansion of the instantaneous frequency distribution.
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