全局耦合相位振子的双曲角统计
Hyperbolic angular statistics for globally coupled phase oscillators
摘要：
我们分析讨论了一个乘性噪声概括的Kuramoto-Sakaguchi动力学的组装的全球耦合相位振荡器。在平均场的限制，所得到的类不变的措施符合一个广义的，两个参数的家庭的角度冯米塞斯概率分布，这是由退出法律从单位盘的双曲漂移布朗运动。我们的动力学提供了一个简单的，但易于分析的概括Kuramoto-Sakaguchi动力学与两个控制参数。我们推导出一个精确的和非常紧凑的两个控制参数之间的关系在相位振荡器同步的发病。
英文摘要：
We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean field limit, the resulting class of invariant measures coincides with a generalized, two parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.
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