Characterizing an ensemble of interacting oscillators: the mean-field variability index.
Characterizing an ensemble of interacting oscillators: the mean-field variability index.
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表征相互作用振荡器的集合：平均场变异指数。
DOI：
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发表时间：
2013
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通讯作者：
A. Stefanovska
中科院分区：
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作者：
L. Sheppard;Alison C. Hale;S. Petkoski;Peter V. E. McClintock;A. Stefanovska
我们介绍了一种根据平均场可变性指数κ来描述相互作用振子集合的方法，这是一个无量纲参数，定义为振子平均场的方差r除以r的均方。基于整体平均场是大量振子的总和的假设，每个振子对总信号的贡献很小，我们表明κ取决于振子之间的相互作用。与它们的数量或光谱特性无关。对于纯随机相量或非相互作用的振子集合，κ收敛于0.215。相互作用推动κ向不同方向移动：当存在振荡器间相位相干时，κ降低；当完全相位同步时，κ趋于零；当幅度同步或间歇同步时，κ升高。我们计算了几个不同情况下的κ，以说明它的效用，使用数值模拟数据和脑电图信号从人类受试者的大脑在清醒时，在麻醉时，在经历癫痫发作。
We introduce a way of characterizing an ensemble of interacting oscillators in terms of their mean-field variability index κ, a dimensionless parameter defined as the variance of the oscillators' mean field r divided by the mean square of r. Based on the assumption that the overall mean field is the sum of a very large number of oscillators, each giving a small contribution to the total signal, we show that κ depends on the mutual interactions between the oscillators, independently of their number or spectral properties. For purely random phasors, or a noninteracting ensemble of oscillators, κ converges on 0.215. Interactions push κ in different directions: lower where there is interoscillator phase coherence, tending to zero for complete phase synchronization, or higher for amplitude synchronization or intermittent synchronization. We calculate κ for several different cases to illustrate its utility, using both numerically simulated data and electroencephalograph signals from the brains of human subjects while awake, while anesthetized, and while undergoing an epileptic fit.