Last modified: Feb 18, 2017
Cybernetics, Kuramoto, Heart Rate Variability, Live
Complexity Training (EEG Biofeedback)
IIn addition to creating cybernetics, a great deal of signal analysis, and
doing the first qEEG, Norbert Wiener speculated that the brain
functioned best when its slow and fast electrical oscillators were “pulled”
toward a single control frequency, namely 10 Hz (cycles per second) .
The 10 Hz brain wave (EEG) is a harmonic of the 0.1 Hz body wave
called the Mayer-Traube-Herring wave. The frequency 0.1 cycles per
second is the same thing as 6 cycles per minute. The neural networks of
the brain developed in an environment shaped by this rhythm. It is the
resonant frequency observed in heart rate variability (HRV) studies.
Here we will talk about the “power spectral displays” of the EEG and the
HRV signals. The power spectral display (PSD) is a graph that shows
the amounts of power produced in the low, medium, and high frequency
In the illustration to the left you see
the natural organizing tendency of
the EEG represented by the arrows.
This organization is best seen in the
eyes closed EEG. The organization
obeys the Constructal Law of Physics
and generates complexity. The
dissipation of the EEG during
sickness behavior or during
intrusions of sleep fragments is
primarily a flow reversal into the lower and upper alpha skirts.  Live
Complexity Training is a type of EEG biofeedback (neurofeedback) that
monitors dissipation of energy into the alpha skirts and trains toward
visible increases in the complexity of the EEG.
The Graphs on the left were
produced by the EM Wave
Pro during heart rate
variability (HRV) biofeedback.
These graphs may change
rapidly during a session. They
show the power spectral
display - the amount of
energy produced by low,
medium and high frequencies
- that contribute to the
moment-by-moment changes in heart rate. The top graph shows my
PSD centered at the resonant frequency. The lower graph shows a client
who has lost central (0.1 Hz) control and could reasonably be said to
have one foot on the gas (sympathecotonia) and one foot on the brake
Here we see the power dissipated in
the EEG at various frequencies in the
healthy CON (green) and in three
types of sickness behavior. “DD” is
depressive disorder, “SSD” is
schizophrenia spectrum disorder,
“OCD” is obsessive-compulsive
disorder. For our purposes they can
all be called “sickness behavior.
There is a clear difference in the EEG
patterns of wellness and sickness
behavior. With increasing sickness
behavior the EEG shows 1) loss of a
sharp 10 Hz control signal; and 2) increased dissipation of energy in the
upper and lower alpha skirts and in the low and high frequency bands in
Note how as “frequency pulling” fails to maintain the sharp 10 Hz peak,
the amount of energy dissipated (wasted) in the lower and upper alpha
skirts increases. At the same time the complexity of the EEG decreases
and is replaced by redundancies easily identifiable in the raw EEG and
on the qEEG spectral display during neurofeedback. Similar patterns are
also described by Ulrich  as a disturbance of normal “vigilance”
mechanisms. I equate this particular form of EEG vigilance with
complexity, both in the EEG and in the behavioral repetoire.
Here we are talking about the loss of “frequency pulling” in sickness
behavior. Wiener was not able to mathematically model this behavior in
his lifetime. Since the introduction of the Kuramoto oscillator in the
1980s it has been shown that frequency pulling self-organizes when
individual oscillators share certain data [5, 6].
In fibromyalgia, for example, the heart rate variability curve is shifted to
the left (the lower HRV skirt) and the EEG is also shifted toward the left
(the lower alpha skirt). 
Kuramoto Oscillators - the Sizzle, the Tsunami, and the
Sickness Behavior EEG
In a moment we will look at an animation of Kuramoto oscillators
displaying 3 different types of behavior that I call 1) Sizzle, 2) Tsunami
and 3) Sickness. Sizzle occurs all over the healthy brain with eyes open.
Tsunami occurs in the healthy posterior cortex with eyes closed.
Sickness behavior occurs anywhere but is especially significant in the
midline. These patterns are easily identified by beginners on the spectral
display and in the raw EEG during neurofeedback. The Kuramoto
oscillators are described below as though they were 9 runners running
clockwise around a track. They could also represent electrically charged
particles running in cycles in and out of neurons and measured by scalp
This first illustration shows the cortical EEG “sizzle” of wellness behavior.
It is characterized by increased complexity and disappearance of any
clear patterns (redundancies). This is a special type of complexity
generated by self-organized criticality . Despite the apparent lack of
any patterns in the complex EEG, it displays self-similarity over-time
It is a result of each neuron performing individualized functions and
exhibiting its own rhythm. In this state, at any particular time, there are
about as many regions in a positively charged state as in a negatively
charged state, so the EEG amplitude is low-voltage (desynchronized)
and exhibits its characteristic sizzle. Libenson describes the sizzle as
“non-descript” . If you zoom into the complex wave you will not see
smooth curves as a result of the magnification. Instead you will see
constant unfolding of complexity. This is the opposite of what happens
when you zoom into the EEG of sickness behavior and see the smooth
curves of redundant slow waves and fast wave (below).
This next graphic illustrates what I call the “Tsunami”. In wellness
behavior with eyes open there is characteristic sizzle all over the cortex.
But with eyes closed the posterior cortex exhibits the tsunami waves of
alpha called the posterior dominant rhythm. The large amplitudes are
produced by the phase synchronization of a large number of neurons.
This next graphic illustrates the appearance of the EEG in sickness
behavior. There is dissipation of EEG energy into the lower and upper
alpha skirts. Unlike the complex “sizzle” of wellness behavior, when you
zoom in on the EEG of sickness behavior you see smooth curves of the
underlying slow waves in the lower alpha skirt. You also see the
redundant fast waves, such as beta spindles, riding on the slow waves.
The self-similarity that is observed when you zoom in or out of a
complex wave is absent in the EEG of sickness behavior. The loss of
long range temporal correlation (self-similarity over time) and the loss of
scale-free dynamics affects timing and memory. This is the characteristic
appearance of the EEG in inflammation, sleep deprivation, methylation
disorders, oxidative stress, addiction, degeneration and so forth.
Please click below to download a video of the Kuramoto Oscillator -
Sizzle, Tsunami and Sickness Behavior.
mp4 format, approx 6.72 MB, with audio.
 Strogatz S (2003) - Sync: How Order Emerges from Chaos in the
Universe, Nature, and Daily Life. Hyperion, N.Y.
 Ulrich G (2013) - The Theoretical Interpretation of
Electroencephalography (EEG). BMed Press, USA.
 Dailey D (2016) - Complexity, Canonical Sickness Behavior and EEG
Biofeedback. Bradley University Super Brain Summit, April 29, 2016.
 Schulman JJ, et al (2011) - Imaging of thalamocortical dysrhythmia in
neuropsychiatry. Frontiers in Human Neuroscience, 29 July. [ Free Full
 Lim M, et al (2016) - Increased Low- and High-Frequency Oscillatory
Activity in the Prefrontal Cortex of Fibromyalgia Patients. Frontiers in
Human Neuroscience, 14 March. [ Free Full Text ]
 Ibanez-Molina AJ, et al (2016) - Neurocomputational Model of EEG
Complexity during Mind Wandering. Front Comput Neurosci. 2016 Mar
4;10:20 [ Free Full Text ]
 Breakspear M, et al (2005) - Dynamics of a neural system with a
multiscale architecture, Phil Trans R Soc B 360, 1051-1074. [ Free Full
 Bak P (1999) – How Nature Works: The Science of Self-Organized
Criticality. Copernicus / Springer-Verlag, NY.
 Libenson MH (2010) - Practical Approach to Electroencephalography.
Saunders, Elsevier. p 6.