### 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 language | English (US) |
---|---|

Article number | 033108 |

Journal | Chaos |

Volume | 21 |

Issue number | 3 |

DOIs | |

State | Published - Jul 19 2011 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Chaos*, vol. 21, no. 3, 033108. https://doi.org/10.1063/1.3615642

}

TY - JOUR

T1 - A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy

AU - Osorio, Ivan

AU - Lai, Ying-Cheng

PY - 2011/7/19

Y1 - 2011/7/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053387588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053387588&partnerID=8YFLogxK

U2 - 10.1063/1.3615642

DO - 10.1063/1.3615642

M3 - Article

C2 - 21974643

AN - SCOPUS:80053387588

VL - 21

JO - Chaos (Woodbury, N.Y.)

JF - Chaos (Woodbury, N.Y.)

SN - 1054-1500

IS - 3

M1 - 033108

ER -