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I've repeatedly come across the claim that brain dynamics operate near the edge of chaos, but usually they do not give any useful sources on how we actually know this.

I'm also aware that there are theoretical models that such dynamics are optimal in terms of information transfer, memory storage, etc and I find it plausible that evolution would try to get us somewhere in that region to the extent possible.

But what precise evidence do we have from brain measurements or realistic brain models that the dynamics are actually near the edge of chaos?

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    $\begingroup$ I've never heard of that claim. Can you provide us with one of your, apparently numerous sources? $\endgroup$ – AliceD Jul 6 '18 at 21:24
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    $\begingroup$ For example this article based on this research. Which of course would be one piece of evidence I'm looking for, but by itself it's pretty weak. $\endgroup$ – qeschaton Jul 7 '18 at 18:13
  • $\begingroup$ Given that you do know the studies related to this (the other one being pnas.org/content/103/51/19518 cited in the one you mentioned), it seems to me this question is more of a "I don't understand this topic". But just from the above, I don't know what you don't understand. $\endgroup$ – Fizz Jul 7 '18 at 18:54
  • $\begingroup$ I some few studies related to this but I find the weight of evidence that I know of wanting so I was curious what other evidence there is. $\endgroup$ – qeschaton Jul 7 '18 at 19:03
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    $\begingroup$ I fend these wanting because these papers use some abstract models which don't exactly have a lot to do with actual brain dynamics to suggest some observables they'd expect to see in the actual brain. Which they do. By themselves I don't find these pieces of evidence particularly compelling. So what I'd be looking for is either more direct evidence (e.g. can we measure 'avalanches' in the brain itself?) or more weak pieces of evidence which support the claim (e.g. maybe 1/f EEG spectrum is exactly what you'd expect from critical dynamics). $\endgroup$ – qeschaton Jul 8 '18 at 15:59
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Dynamical systems (basically all of them) display a wide repertoire of dynamics when tuned close to criticality (https://en.wikipedia.org/wiki/Critical_phenomena). In this range, organized patterns of activity emerge, close to those that we find when looking at statistical dependencies between time series recording (at least partially) brain activity.

Long range correlations also emerge in this phase.

So, it's true that dynamical models tuned close to criticality better fit brain activity. On the other hand saying that "brain activity is critical" is a logical fallacy, since we are giving to the modelled system properties of the model.

(chaos is a close concept, stressing the dependency on initial conditions, but in this case I think that criticality is more relevant).

See, among other things, this scientific yet accessible paper

Beggs, J. M., & Timme, N. (2012). Being Critical of Criticality in the Brain. Frontiers in Physiology, 3. doi:10.3389/fphys.2012.00163

https://www.frontiersin.org/articles/10.3389/fphys.2012.00163/full

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