🚀 go-pugleaf

Recently, Lester Ingber asked me what my assessment was of the evidence
for and against chaotic dynamics in the brain. I couldn't provide a
thoughtful answer at the time, since I had not read the relevant
literature. Since then, I've had an opportunity to do that, particularly
the Skinner papers and the survey paper by Abarbanel et al on data
analysis of observations of possibly chaotic physical systems. My take
now is that with certain caveats, I believe the evidence supports the
existence of chaotic dynamics in the brain.

The first caveat concerns the nature of the data. Any finite set of
measurements can be misleading, particularly for nonlinear systems. To
demonstrate the existence of a strange attractor, several passes
through the attractor are needed at minimum.

Second, biological systems are noisy (possibly high-dimensional
non-linear dynamics), and that noise can confound the evidence.

Third, the dynamics of the brain are non-stationary. The measurement
algorithms in common use assume stationarity.

Fourth, the attractor in a portion of the brain at any point in time
depends on at least three factors: 1) the current afferent signal, 2)
the current expectation in terms of which signal patterns are primed
for classification, and 3) the local structure of the brain. Hence, you
cannot speak of chaotic dynamics in a general sense, but rather of
whether the local dynamics ->now<- reflect a strange attractor.

Given those caveats, I am of the opinion that Mitra and Skinner (1992,
"Low-Dimensional Chaos Maps Learning in a Model Neuropil (Olfactory
Bulb)," Integrative Physiological and Behavioral Science,
October-December, 1992, Vol. 27, No. 4, 304-322) give reason to
believe that the brain can instantiate local attractors with fractal
dimension. There appears to be sufficient data collected during the
period of existence of individual attractors to allow estimation of the
correlation dimension, the estimator algorithm appears to be robust
against noise, transients appear not to be an issue (due to the design
of the algorithm), and a degree of repeatability appears to be present.
Granted, there are difficulties with using real-world data to
demonstrate presence of chaos (as Abarbanel, et al., so ably discuss),
but Mitra and Skinner appear to have addressed most of those issues.

  --
Harry Erwin
Internet: herwin@gmu.edu 
Working on Katchalsky nets....