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Characterizing an ensemble of interacting oscillators: the mean-field variability index

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Article numberARTN 012905
<mark>Journal publication date</mark>9/01/2013
<mark>Journal</mark>Physical Review E
Issue number1
Number of pages11
<mark>Original language</mark>English


We introduce a way of characterizing an ensemble of interacting oscillators in terms of their mean-field variability index kappa, 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 kappa 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, kappa converges on 0.215. Interactions push kappa 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 kappa 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. DOI: 10.1103/PhysRevE.87.012905