19 Citations (Scopus)

Abstract

We present a general method to analyze multichannel time series that are becoming increasingly common in many areas of science and engineering. Of particular interest is the degree of synchrony among various channels, motivated by the recognition that characterization of synchrony in a system consisting of many interacting components can provide insights into its fundamental dynamics. Often such a system is complex, high-dimensional, nonlinear, nonstationary, and noisy, rendering unlikely complete synchronization in which the dynamical variables from individual components approach each other asymptotically. Nonetheless, a weaker type of synchrony that lasts for a finite amount of time, namely, phase synchronization, can be expected. Our idea is to calculate the average phase-synchronization times from all available pairs of channels and then to construct a matrix. Due to nonlinearity and stochasticity, the matrix is effectively random. Moreover, since the diagonal elements of the matrix can be arbitrarily large, the matrix can be singular. To overcome this difficulty, we develop a random-matrix based criterion for proper choosing of the diagonal matrix elements. Monitoring of the eigenvalues and the determinant provides a powerful way to assess changes in synchrony. The method is tested using a prototype nonstationary noisy dynamical system, electroencephalogram (scalp) data from absence seizures for which enhanced cortico-thalamic synchrony is presumed, and electrocorticogram (intracranial) data from subjects having partial seizures with secondary generalization for which enhanced local synchrony is similarly presumed.

Original languageEnglish (US)
Article number033108
JournalChaos
Volume21
Issue number3
DOIs
StatePublished - Jul 19 2011

Fingerprint

epilepsy
time series analysis
Epilepsy
Phase Synchronization
Time series analysis
Synchrony
Time Series Analysis
Random Matrices
synchronism
Synchronization
seizures
matrices
time synchronization
electroencephalography
complex systems
determinants
dynamical systems
eigenvalues
Stochasticity
nonlinearity

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy. / Osorio, Ivan; Lai, Ying-Cheng.

In: Chaos, Vol. 21, No. 3, 033108, 19.07.2011.

Research output: Contribution to journalArticle

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