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λ(+) were reported in awake relaxed subjects and were lost in deep sleep (Stage IV) and coma (advanced Jakob-Creutzfeld disease), suggesting that level of consciousness correlated positively with amount of orbital divergence (Gallez and Bablioyantz, 1991). A "pathologically low" leading λ(+) was also found to be characteristic of the EEG of patients with Alzheimer's syndromes (Jeong et al, 1998). Technically defined sleep stages (I, II, III, IV, REM) were found to correlate well with the values of the leading λ(+) of the EEG in normal subjects (Fell et al, 1993; 1996; Pradhan and Sadasivan, 1996). EEG recordings during problem solving sometimes, but not always, demonstrated a relationship between values of λ(+) and the kind or amount of load of the task (Micheloyannis et al, 1998; Popivanovov et al, 1998; Meyer-Lindenberg et al, 1998). Both emotionally positive and negative videos increased the value of the leading λ(+) (Aftanos et al, 1997) as did computer generated music with sounds that exploited a "pleasing" hierarchical, 1/f but not an "unpleasant" 1/f 2 frequency spectrum (see previous section about power law scaling) (Jeong et al, 1998). The EEG theta rhythm of "day dreaming" manifested a lower λ(+) than the "relaxed alert awake" alpha rhythm (Roschke et al, 1997). Relationships between the Lyapounov spectra demonstrated both regional independence and task-related dependence in the magnetoencephalography record in man (Kowalik and Elbert, 1995).

These and other studies suggest that divergence rate of orbits on a geometrically reconstructed attractor is a subtle measure, which can be quantified as a continuous variable and which has been found to be useful in a variety of neuroscience-related, experimental contexts. The range includes the characterization of the discharge pattern of a single somatic or renal sympathetic nerve fiber (Gong et al, 1998; Zhang and Johns, 1998); quantifying the results of perturbing autonomic nervous system activity, for examples, exercise, atropine and propranolol decrease λ(+) in the cardiac interbeat interval attractor (Hagerman et al, 1996) and interference with the function of the baroreflex or clonidine alters the λ(+) in the blood pressure attractor in man and animals (Wagner et al, 1996;

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