Nonlinear Dynamical Analysis: Application to EEG Sleep Analysis

Abstract

Nonlinear dynamical analysis techniques have been widely used for EEG analysis. The correlation dimension based upon the correlation is one of the most commonly used measures which quantifies the active degrees of freedom or the complexity of the dynamical system on the attractor. This article aims to provide an overview of the basic concepts of nonlinear dynamical analysis, and also to demonstrate its application in EEG sleep analysis. As one of the evidences, it is shown that there is a decrease in the correlation dimension (i.e., a loss in the complexity of the underlying dynamics of the neuronal networks in the brain) from lighter to deeper sleep stages. The use of the nonlinear dynamical analysis can be viewed in two aspects. In one aspect, the lower correlation dimension of the EEG suggests that the neuronal networks are more strongly coupled at deeper sleep stage. In another aspect, the substantial differences of the correlation dimensions of the EEG associated with various sleep stages can be used for sleep stage discrimination.