Friday 26 June 2015

Do you have a chaotic brain?

There is some (disputed) biological evidence [1,2,3] that what goes on inside your brain is chaotic (I could find plenty of real evidence for this in my case!) But this is not referring to the common meaning of the term 'chaos', which is normally used to describe something which is highly disorganised. On the contrary, in this context we are using the term 'chaos' in its specialist mathematical sense to describe something which is highly organised, but difficult to predict.


Early in my research career, I became interested in the possibility that brain activity is chaotic in this mathematical sense. I pondered what this might mean. Does this chaos offer any advantage to the brain in terms of the memories it can store and retrieve, or in terms of how it processes information? One thing that is notable about chaotic systems is that they are dynamic, restless, ceaselessly moving, creating new paths, new possibilities, and yet remaining constrained, bounded in a small sub-region of their potential 'space'. Sounds impossible? Have a look at this:


Here you see a classic chaotic system called the Lorenz attractor [4]. The light blue line illustrates the two winged sub-region that this chaotic systems is constrained within (i.e. its 'attractor'). The red point is a particular state of the system which, as you will see, starts far away from the attractor, but moves over time towards it and then continues to describe a path around it. Although this system is constrained to its two winged attractor, it will never stop moving, it will never be in exactly the same point twice on its attractor and it will continuously trace new paths (transients) as it goes along. Pretty cool!

Although the system will never be at exactly the same point twice (i.e. it will never be in exactly the same state more than once), it will come very close to points that it had previously visited, forming complex loop-like structures that are called 'unstable periodic orbits' (UPOs - see image on the right, taken from [5]).

Another remarkable feature of a chaotic attractor is that it can embed an infinite number of these UPOs. One question we asked ourselves early on in this research was, what if each of these UPO's represented a memory of the network [5]? If this could be achieved, then the memory capacity of the network (and by implication the brain) would also be theoretically infinite.

This begs lots of questions, most of which we have been unable to answer. However, in my next blog, I will begin to outline some of the work I did with colleagues at Oxford Brookes University on developing chaotic models of neural information processing in the brain.

References

[1]  Babloyantz, A., Lourenco, C., 1996. Brain chaos and computation. International Journal of Neural Systems 7, 461–471.

[2] Freeman,W.J., 1987. Simulation of chaotic eeg patterns with a dynamic model of the

olfactory system. Biological Cybernetics 56, 139–150.

[3] Freeman, W.J., Barrie, J.M., 1994. Chaotic oscillations and the genesis of meaning
in cerebral cortex. In: Buzsaki, G., et al. (Eds.), Temporal Coding in the Brain.

Springer–Verlag, Berlin, pp. 13–37.

[4] Lorenz, Edward Norton (1963). "Deterministic nonperiodic flow". Journal of the Atmospheric Sciences 20 (2): 130–141.

[5] Crook, N.T. & olde Scheper, T. (2002) Adaptation Based on Memory Dynamics in a Chaotic Neural Network.  Cybernetics and Systems 33 (4), 341-378.

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