What does "a critical point or phase transition [of the] electrodynamics of the cortex" mean? Electricity doesn't have "phases" AFAIK (well there's two/three-phase power but I don't think that's what they're talking about).
https://en.wikipedia.org/wiki/Critical_exponent
The concept of phase transition is broader than the phases of matter.
At low differentials there’s no convection just conduction, as you raise the temperature difference you get a stable single circulation loop which is well behaved, continue further and you get a tempest of circulations coming and going in an entirely unpredictable manner.
There are distinct phase transitions between each of these states.
Another one is a forced double pendulum. With just a little periodic force they swing gently back and forth, with a lot they do constant crazy unpredictable loops around each other.
* A mathematician explains what Foundation gets right about predicting the future (spoiler: critical points!): https://www.sciof.fi/a-mathematician-explains-psychohistory/
And if you're still interested, there's a more in-depth explanation with mathematical formulas and all. Even if I understood only 10-20% of what Ken Wilson was talking about, he gives a lucid motivation for why critical points are important and why they can be found in practice using renormalization groups, and not computer simulations:
* Ken Wilson's Nobel Prize lecture: https://www.nobelprize.org/uploads/2018/06/wilson-lecture-2....
https://mitpress.mit.edu/books/dynamical-systems-neuroscienc...