Characterizing an ensemble of interacting oscillators: The mean-field variability index (original) (raw)
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Chaos: An Interdisciplinary Journal of Nonlinear Science, 2005
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization. PACS numbers: 05.45.-a, 05.45.Tp An interdisciplinary problem of detecting interaction between oscillatory systems solely from their time realizations has attracted attention of researchers for a long time. Several approaches to its solution have been suggested within the framework of linear time series analysis and information theory. The most well-known of them are cross-correlation function, coherence function, and mutual information function, which are typically capable of detecting only the presence of interdependence. To detect coupling directionality, their generalizations exist, such as Granger causality 2 , Geweke's spectra 3 , and similar information-theoretic concepts 4,5 . Recently, there have been developed new approaches in nonlinear dynamics to reveal the presence of nonlinear interaction and its directionality. These nonlinear techniques are based either on analysis in state spaces 6-13 or investigation of phase dynamics 14-20 . The latter set of approaches includes an evolution map approach, based on modeling phase dynamics of 2 the systems 17,18 , and its extension for the case of relatively short time series 1 . The latter technique is shown to be often more sensitive to weak coupling than state space approaches, especially for the practically important case of short signals 21 . In addition, expressions for the confidence bands have been developed for the coupling estimators of Ref. 1 that increases reliability of the results. But all the formulas are rigorously valid only for weakly nonlinear and weakly coupled phase oscillators under the influence of independent sources of Gaussian white noise. In the present paper, we investigate practical limits of applicability of these formulas and show in numerical experiments that they are quite wide. Finally, application of the estimators to an intracranial EEG recording from an epileptic patient is presented.
Characterization of Synchronization in Interacting Groups of Oscillators: Application to Seizures
Biophysical Journal, 2008
We investigate the emergence of synchronization in two groups of oscillators; one group acts as a synchronization source, and the other as the target. Based on phase model simulations, we construct a synchrony index (SI): a combination of intra-and intergroup synchronies. The SI characterizes the extent of induced synchrony in the population. We demonstrate the usefulness of the measure in a test case of mesial temporal lobe epilepsy: the SI can be readily calculated from standard electroencephalographic measurements. We show that the synchrony index has a statistically significant increased value for the ictal periods and that the epileptic focus can be located by identifying the most synchronous pairs of electrodes during the initial part of ictal period of the seizure. We also show that it is possible in this pilot case to differentiate clinical and subclinical seizures based on the dynamical features of the synchronization. The synchronization index was found to be a useful quantity for the characterization of ''pathological hypersynchronization'' within a well-characterized patient with mesial temporal lobe epilepsy and thus has potential medical value in seizure detection, localizing ability, and association with later surgical outcome.
We investigate patterns of collective phase synchronization in brain activity in awake, resting humans with eyes closed. The alpha range of human electroencephalographic activity is characterized by ever-changing patterns, with strong fluctuations in both time and overall level of phase synchronization. The correlations of these patterns are reflected in power-law scaling of these properties. We present evidence that the dynamics underlying this fluctuation is type-I intermittency. We present a model study illustrating that the scaling property and the collective intermittent dynamics are emergent features of globally coupled phase oscillators near the critical point of entering global frequency locking.
NeuroImage, 2006
The quantification of phase synchrony between brain signals is of crucial importance for the study of large-scale interactions in the brain. Current methods are based on the estimation of the stability of the phase difference between pairs of signals over a time window, within successive frequency bands. This paper introduces a new approach to study the dynamics of brain synchronies, Frequency Flows Analysis (FFA). It allows direct tracking and characterization of the nonstationary time-frequency dynamics of phase synchrony among groups of signals. It is based on the use of the one-to-one relationship between frequency locking and phase synchrony, which applies when the concept of phase synchrony is not taken in an extended Fstatistical_ sense of a bias in the distribution of phase differences, but in the sense of a continuous phase difference conservation during a short period of time. In such a case, phase synchrony implies identical instantaneous frequencies among synchronized signals, with possible time varying frequencies of synchronization. In this framework, synchronous groups of signals or neural assemblies can be identified as belonging to common frequency flows, and the problem of studying synchronization becomes the problem of tracking frequency flows. We use the ridges of the analytic wavelet transforms of the signals of interest in order to estimate maps of instantaneous frequencies and reveal sustained periods of common instantaneous frequency among groups of signal. FFA is shown to track complex dynamics of synchrony in coupled oscillator models, reveal the time-frequency and spatial dynamics of synchrony convergence and divergence in epileptic seizures, and in MEG data the large-scale ongoing dynamics of synchrony correlated with conscious perception during binocular rivalry. D
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
Physical Review Letters, 2007
We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always result from arbitrary initial conditions, irrespective of the details of the oscillators.
IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2018
Spatiotemporal evolution of synchrony dynamics among neuronal populations plays an important role in decoding complicated brain function in normal cognitive processing as well as during pathological conditions such as epileptic seizures. In this paper, a non-linear analytical methodology is proposed to quantitatively evaluate the phase-synchrony dynamics in epilepsy patients. A set of finite neuronal oscillators was adaptively extracted from a multi-channel electrocorticographic (ECoG) dataset utilizing noise-assisted multivariate empirical mode decomposition (NA-MEMD). Next, the instantaneous phases of the oscillatory functions were extracted using the Hilbert transform in order to be utilized in the mean-phase coherence analysis. The phase-synchrony dynamics were then assessed using eigenvalue decomposition. The extracted neuronal oscillators were grouped with respect to their frequency range into wideband (1-600 Hz), ripple (80-250 Hz), and fast-ripple (250-600 Hz) bands in order to investigate the dynamics of ECoG activity in these frequency ranges as seizures evolve. Drug-refractory patients with frontal and temporal lobe epilepsy demonstrated a reduction in phase-synchrony around seizure onset. However, the network phase-synchrony started to increase towards seizure end and achieved its maximum level at seizure offset for both types of epilepsy. This result suggests that hypersynchronization of the epileptic network may be an essential self-regulatory mechanism by which the brain terminates seizures.
Physica D: Nonlinear Phenomena, 2000
We apply the concept of phase synchronization of chaotic and/or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms (EEGs) recorded from patients with temporal lobe epilepsy. Using the mean phase coherence as a statistical measure for phase synchronization, we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity. In particular, we observe distinct differences in the degree of synchronization between recordings from seizure-free intervals and those before an impending seizure, indicating an altered state of brain dynamics prior to seizure activity.
Synchronization by uncorrelated noise: interacting rhythms in interconnected oscillator networks
Scientific Reports
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. How do multiple such rhythms interact with each other? Do these collective oscillations synchronize like individual oscillators? We show that this is not the case: for strong, inhibitory coupling rhythms can become synchronized by noise. In contrast to stochastic synchronization, this new mechanism synchronizes the rhythms even if the noisy inputs to different oscillators are completely uncorrelated. Key for the synchrony across networks is the reduced synchrony within the networks: it substantially increases the frequency range across which the networks can be entrained by other networks or by periodic pacemaker-like inputs. We demonstrate this type of robust synchronization for different classes of oscillators and network connectivities. The synchronization of different population rhythms is expected to be relevant for brain rhythms.
PloS one, 2016
Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for...
Routes to synchrony between asymmetrically interacting oscillator ensembles
Physical Review E
We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurrence of the routes is determined by phase asymmetry. The identification of these phenomena offers new insight into synchrony between oscillator ensembles and suggest new ways in which it may be controlled.