I think I might have some sort of direction, as of this morning, though I'm afraid I'm flying a bit wide of... things, at this point. Any thoughts would be greatly appreciated.
On one end of the spectrum, we have a simple sigmoid perceptron pair which is analytically proven to have regions of period doubling and all that chaotic goodness.
On the other end of the spectrum, we have the squishy human brain. The squishy human brain has been shown to have elements of chaotic behavior, most interestingly in the spike trains.
The spike trains (time sequences of essentially binary neural "spikes", or firings) appear to be inherently chaotic. This chaos is encoded in the intervals between spike trains. Where this gets really interesting is that one paper I read did statistical voodoo showing that the chaos inherent in these trains is mathematically resolvable. If the chaotic spike train has this statistical voodoo applied to it, it retains its strength; while if the same spike intervals are reordered randomly, the statistical voodoo fades it to oblivion.
Unfortunately, the chaotic goodness of the simple sigmoid perceptron pair has not been mapped in any way that I can find to the chaotic goodness of the squishy human brain.
So I propose to give an overview of all related factoids while attempting to tie, in a "there exists" sort of manner, one to the other. Preferably with a couple of applets and pictures.
Ideally I will be able to create spike trains out of the simple sigmoid perceptron pair which are immune to the statistical voodoo, but break down in a similar manner when reordered.
Whether that will mean anything is anyone's guess.