AUTHOR=Gao Jianbo 

TITLE=Multiscale Analysis of Biological Data by Scale-Dependent Lyapunov Exponent

JOURNAL=Frontiers in Physiology

VOLUME=volume 2 - 2011

YEAR=2012

URL=https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2011.00110

DOI=10.3389/fphys.2011.00110

ISSN=1664-042X

ABSTRACT=Physiological signals often are highly nonstationary and multiscaled
--- depending upon the scale at which they are examined, they may
exhibit different behaviors, such as
nonlinearity, sensitive dependence on small disturbances, long
memory, and extreme variations. Such data have been  accumulating
rapidly in all areas of
health  sciences.
It is very desirable to characterize the different
behaviors of such signals on a wide range of scales simultaneously.
The scale-dependent Lyapunov exponent (SDLE) is  capable of such a
fundamental task. In particular, SDLE can readily
characterize all known types of data, including
deterministic  chaos, noisy chaos,
random $1/f^{\alpha}$
processes,  stochastic limit cycles, among others. It can also
readily deal with many types of nonstationarity and
detect intermittent chaos.
To illustrate its effectiveness in analyzing physiological data,
we consider detection of epileptic seizures from EEG and certain
cardiac disease from heart rate variability (HRV) data.
In particular, we show that commonly
used complexity measures for physiological data, including those
from information theory, chaos theory,
 and random fractal theory, can all be related to the
values of the SDLE at specific scales, and therefore,
SDLE can act as the basis for a unified theory of
multiscale analysis of complex data.