Information Technology Reference
In-Depth Information
Awake, eyes open
Awake, eyes closed
Sleep stage 2
Sleep stage 4
REM sleep
Epileptic seizure (absence)
Comatous (CJ disease)
0.
1.00
2.00 3.00
Time (sec)
4.00
5.00
Figure 4.11.
EEG signals and phase portraits during different brain states in humans. Left, 5 seconds of EEG
activity in different brain states (same amplitude scale); right, two-dimensional phase portraits of
each signal constructed using ART (see the text). Reproduced from [
9
] with permission.
the clarity of the mapping in Figure
4.10
, they do not fill the phase space as would a
purely random time series.
Complex dynamical webs have provided a new kind of insight into the evolution of
such networks. As stated by Joe Ford [
21
],
... Determinism means that Newtonian orbits exist and are unique, but since existence-uniqueness
theorems are generally not constructive, they assert nothing about the character of the New-
tonian orbits they define. Specifically, they do not preclude a Newtonian orbit passing every
computable test for randomness or being humanly indistinguishable from a realization of a truly
random process. Thus, popular opinion notwithstanding, there is absolutely no contradiction in
the term “deterministically random.” Indeed, it is quite reasonable to suggest that the most general
definition of chaos should read: chaos means deterministically random ...
Thus, if nonlinearities are ubiquitous then so too must be chaos. This led Ford to
speculate on the existence of a generalized uncertainty principle based on the notion
that the fundamental measures of physics are actually chaotic. The perfect clocks and
meter sticks of Newton are replaced with “weakly interacting chaotic substitutes” so
