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brain enzyme kinetics (Mandell, 1984) and single neuron firing patterns (Selz and
Mandell, 1991) to human psychomotor and cognitive behavior (Selz, 1992; Selz and
Mandell, 1993).

The Leading λ(+) of Some Biologically Relevant Time Series

An early application of a simplified form of leading Lyapounov exponent to
brain data involved the computation of the one dimensional averaged slope of in
vitro studies of psychopharmacological drug and peptide effects on time series of
catecholamine and indoleamine biosynthetic enzyme activities studied at
physiological, far-from-equilibrium reactant concentrations (Russo and Mandell,
1984b; Knapp and Mandell, 1984). A contemporaneous study also suggested the
influence of differences in initial conditions for pharmacokinetic equilibrium times in
drug binding kinetics by proteins (Bayne and Hwang, 1985).

The most extensive applications to the clincial neurosciences of the
Lyapounov measure of the exponential divergence of orbital points has involved
reconstructed brain wave attractors from the intracranial or scalp recordings of the
EEG (Duke and Pritchard, 1991; Dvorak and Holden, 1991; Jansen and Brandt,
1993). Space prevents us from surveying more than a small representative set of
the studies (Jansen, 1996). It should be noted, however, that this is an area in
which “state of the art” research has grown quite complicated and somewhat
controversial with respect to technical issues. The choices of the digitizing
frequency of the smooth record, the dimension of the embedding space and time
delays continue to be debated in the context of numerical computations of λ and
dimension measures (Mayer-Kress, 1986; Ott et al, 1994).

Controls for the implicitly required statistical discrimination between
“randomness” and “deterministic chaos” consist of sequence and (Fourier) phase
randomization generating “surrogate data” which conserve the probability
distributions and destroy the correlation properties and attractor geometries (Sauer
et al, 1991; Ott et al, 1994). Since neither bring with them any connections with

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