Neural networks in the brain are evaluated during sleep, and constitute a dynamic system. The electro-encephalogram (EEG) is the principle output time series used to characterize one feature of the underlying dynamics of the neural system that is recorded during sleep. In this study, the authors seek to develop a set of tests to examine the nature of the time series, and to establish the presence of nonlinear dynamics. In particular, they attempt to detect deterministic chaos in the EEG.