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

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 [Formula: see text]-sets, provides an efficient way to classify the data generator mechanism. The second, the [Formula: see text]-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.