Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity

 We tested the hypothesis of whether sleep electroencephalographic (EEG) signals of different time windows (164 s, 82 s, 41 s and 20.5 s) are in accordance with linear stochastic models. For this purpose we analyzed the all-night sleep electroencephalogram of a healthy subject and corresponding Gaussian-rescaled phase randomized surrogates with a battery of five nonlinear measures. The following nonlinear measures were implemented: largest Lyapunov exponent L1, correlation dimension D2, and the Green-Savit measures δ2, δ4 and δ6. The hypothesis of linear stochastic data was rejected with high statistical significance. L1 and D2 yielded the most pronounced effects, while the Green-Savit measures were only partially successful in differentiating EEG epochs from the phase randomized surrogates. For L1 and D2 the efficiency of distinguishing EEG signals from linear stochastic data decreased with shortening of the time window. Altogether, our results indicate that EEG signals exhibit nonlinear elements and cannot completely be described by linear stochastic models. Received: 21 December 1995/Accepted in revised form: 19 March 1996