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Throughout the previous chapters we demonstrated the use
of the dimension and entropy estimators using time series obtained from
models. Here we present some results obtained using
time series from biological processes.
In the human body there are fractal-like structures, e.g. the airways
of the lung, the inner surface of the small intestine and
the blood vessels of the heart.
Likewise, signals produced by physiological systems show
irregular behaviour and we are tempted to investigate whether a
signal is produced by a chaotic system with a strange attractor.
Irregularity and unpredictability of physiological systems are
speculated to be
important features of health, while decreased variability and accentuated
periodicities are associated with disease [Goldberger et al., 1990].
Chaos theory may provide the tools to analyse and classify the variability
of physiological systems. We will try to identify chaotic dynamics behind
biological signals using the methods described in the previous chapters.
In fact, the whole procedure consists of the following steps:
- Take the maximum length for which the dynamics can be regarded
to as stationary. Choose the sampling frequency. This choice will
generally be a compromise between oversampling and the number of points.
Determine the time lag for the phase space reconstruction using
the minimum mutual information criterion.
For more information, see Chapter 6.
- Plot correlation integrals and their numerical derivatives for
increasing embedding dimensions. Identify the scaling regions
by the naked eye.
- Estimate the correlation dimension and entropy, and their variances,
as a function of the embedding dimension using the expressions as
derived with the maximum likelihood approach (see Chapter 5).
- Determine whether the estimated dimension ``saturates'',
i.e. converges to a constant value as a function of the embedding
dimension. If so, determine whether the estimated entropy
converges or not.

In the following sections,
we present results from the analysis of recordings of
the brain activity (electroencephalograms)
and of the respiration.

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