THE CALCULATION OF THE 1ST POSITIVE LYAPUNOV EXPONENT IN SLEEP EEG DATA

To help determine if the EEG is quasiperiodic or chaotic we performed a new analysis by calculating the first positive Lyapunov exponent L1 from sleep EEG data. Lyapunov exponents measure the mean exponential e xpansion or contraction of a flow in phase space. L1 is zero for perio dic as well as quasiperiodic processes, but positive in case of chaoti c processes expressing the sensitive dependence on initial conditions. We calculated L1 for sleep EEG segments of 15 healthy male subjects c orresponding to sleep stages I, II, III, IV and REM (according to Rech tschaffen and Kales). Our investigations support the assumption that E EG signals are neither quasiperiodic waves nor simple noise. Moreover, we found statistically significant differences between the values of Ll for different sleep stages.