DETERMINISTIC CHAOS AND THE 1ST POSITIVE LYAPUNOV EXPONENT - A NONLINEAR-ANALYSIS OF THE HUMAN ELECTROENCEPHALOGRAM DURING SLEEP

Under selected conditions, nonlinear dynamical systems, which can be d escribed by deterministic models, are able to generate so-called deter ministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separat ed for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a determini stic process which should not be mistaken for simple noise. The calcul ation of dimensionality estimates the degrees of freedom of a signal. Nevertheless, it is difficult to decide from this kind of analysis whe ther a process is quasiperiodic or chaotic. Therefore, we performed a new analysis by calculating the first positive Lyapunov exponent L1 fr om sleep EEG data. Lyapunov exponents measure the mean exponential exp ansion or contraction of a flow in phase space. L1 is zero for periodi c as well as quasiperiodic processes, but positive in the case of chao tic processes expressing the sensitive dependence on initial condition s. We calculated L1 for sleep EEG segments of 15 healthy men correspon ding to the sleep stages I, II, III, IV, and REM (according to Rechtsc haffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor a simple noise. Moreover, we found statistically significant differences between the values of L 1 for different sleep stages. All together, this kind of analysis yiel ds a useful extension of the characterization of EEG signals in terms of nonlinear dynamical system theory.