Rainer Engelken
It is fascinating to me how information in the brain is processed by
the coordinated interplay of many neurons. In particular, how neural
activity patterns are shaped by the wiring diagram known as the
connectome, and how changes at this level explain the reorganization
of the collective dynamics during learning, triggered my curiosity. I
am exploring the chaotic dynamics of neural tissue from a dynamical
system perspective. This is rooted in the mathematical field of
ergodic theory.
As it is hard to visualize and imagine a 1000D entangled attractor
living in a 10000D phase space, we sometimes use small networks for
illustration and as a more intuitive approach to our scientific
questions.
Here is a two-dimensional projection of a strange chaotic attractor of the network activity of fifty randomly connected firing-rate neurons. Every state of the network is a point in the fifty-dimensional state space. The two axes are spanning the direction of the largest variance of the chaotic attractor. Grey-values encode the density of states on this two-dimensional slice through the fifty-dimensional state space. The attractor dimensionality indicates that the network activity explores only a small portion of the available fifty-dimensional phase space. Each rate unit has a sigmoidal input-output function and has simple relaxation dynamics. Only through the network interaction complex patterns and chaos can emerge.