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

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Characterizing an ensemble of interacting oscillators: the mean-field variability index. / Sheppard, L. W.; Hale, A. C.; Petkoski, S. et al.
In: Physical Review E, Vol. 87, No. 1, ARTN 012905, 09.01.2013.

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Sheppard LW, Hale AC, Petkoski S, McClintock PVE, Stefanovska A. Characterizing an ensemble of interacting oscillators: the mean-field variability index. Physical Review E. 2013 Jan 9;87(1):ARTN 012905. doi: 10.1103/PhysRevE.87.012905

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Sheppard, L. W. ; Hale, A. C. ; Petkoski, S. et al. / Characterizing an ensemble of interacting oscillators : the mean-field variability index. In: Physical Review E. 2013 ; Vol. 87, No. 1.

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@article{ed21d2f91aed48bfafa7b98fd8758159,
title = "Characterizing an ensemble of interacting oscillators: the mean-field variability index",
abstract = "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",
keywords = "POPULATIONS, COUPLED OSCILLATORS, COMPLEX, SYNCHRONIZATION, BRAIN, KURAMOTO MODEL, DYNAMICS, ANESTHESIA",
author = "Sheppard, {L. W.} and Hale, {A. C.} and S. Petkoski and McClintock, {P. V. E.} and A. Stefanovska",
year = "2013",
month = jan,
day = "9",
doi = "10.1103/PhysRevE.87.012905",
language = "English",
volume = "87",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Characterizing an ensemble of interacting oscillators

T2 - the mean-field variability index

AU - Sheppard, L. W.

AU - Hale, A. C.

AU - Petkoski, S.

AU - McClintock, P. V. E.

AU - Stefanovska, A.

PY - 2013/1/9

Y1 - 2013/1/9

N2 - 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

AB - 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

KW - POPULATIONS

KW - COUPLED OSCILLATORS

KW - COMPLEX

KW - SYNCHRONIZATION

KW - BRAIN

KW - KURAMOTO MODEL

KW - DYNAMICS

KW - ANESTHESIA

U2 - 10.1103/PhysRevE.87.012905

DO - 10.1103/PhysRevE.87.012905

M3 - Journal article

VL - 87

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - ARTN 012905

ER -