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Chaotic Dynamics in Brain Activity: An Approach Based on Cross-Prediction Errors for Nonstationary Signals

Hospital Israelita Albert Einstein, São Paulo/SP 05652-900, Brazil

Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, São Bernardo do Campo/SP 09606-070, Brazil

Swartz Center for Computational Neuroscience, Institute for Neural Computation, University of California San Diego, San Diego/CA 92093-0559, USA

E-mail Address: andre.fonseca@ufabc.edu.br

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Edgard Morya

Edmond and Lily Safra International Institute of Neuroscience, Santos Dumont Institute, Macaiba/RN 59280-000, Brazil

E-mail Address: edgard@isd.org.br

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Edson Amaro, Jr

Hospital Israelita Albert Einstein, São Paulo/SP 05652-900, Brazil

Faculdade de Medicina da Universidade de São Paulo, São Paulo/SP 01246-903, Brazil

E-mail Address: edson.amaro@gmail.com

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https://doi.org/10.1142/S2424922X1840003XCited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue on Adaptive Analysis Applied to Biomedical Data

Abstract

In this work, we developed two novel approaches to characterize dynamical properties of brain electrical activity, based on cross-prediction errors analysis. The first, a test called $γ$ -sets, provides an efficient way to classify the data generator mechanism. The second, the $μ$ -index, considers relevant changes in the dynamics through stationarity checking. These measures are defined by two basic properties of chaotic time series: a set of dense orbits and the similarity between its parts. The accuracy was verified for simulated signals with different dynamical properties and by the relation with other descriptive measures, Lempel–Ziv complexity and Lyapunov exponents. We applied these measures to local field potentials data, acquired from the cerebral cortex of a Wistar rat during a sleep-wake cycle, and point out evidence of deterministic components in the brain electrical activity even if it exhibits a nonstationary signature.

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