Mathematical opinions: serious stuff this time

[Ummon]

http://www.ccsr.uiuc.edu/ucs2008/Arn..._Urbana_08.ppt

Many thanks, anticipately.

[chris_uk_83]

What exactly is it that you want to know? If you want to know if the maths they quote is real then it's pretty difficult to say with any certainty unless you know what the letters actually stand for and you'd have had to have been at the lecture for that. However, the few equations that were there were equations that describe periodic motion, which seems to be what the slides are about so I'd say that it probably does check out.

The actual material seems fairly mundane stuff though, I thought we knew that brain waves changed during different activities or levels of consciousness.

[Ummon]

No need for being there, there are books too. Given that I myself have a pretty suspended judgement on the issue of the lecture, I wanted to hear anything that comes to your mind. But my judgement would be, that the issue of brain wave frequencies there is not as you portray it, a "mundane" matter. There is an attempt of modelization which substitutes previous knowledge of Talamic pacemakers, for example, and several other things.

Anyway, free thoughts, if you have them.

[Playfishpaste]

I don't get how this is novel, different "states of consciousness" (more appropriately the ones discussed here would be called "states of mind" but alright) have always been thought to have different frequencies when represented on an EEG or any oscilloscope voltage plot. I guess thinking of it as a chaotic system is a new touch, but this was already common sense. The brain isn't exactly consistent.

The entire "synchronization" part didn't make any sense to me, did they mean they were trying to synchronize the attractors?

[Ummon]

As far as I can tell, they are stating that the attractors merge under certain circumstances as well. It is difficult to tell judging from a powerpoint, thus I have ordered the old book of his and another too. It seems he is suggesting there is a special kind of chaos in place as well. I cannot judge before a more thorough look.

[Morkonan]

http://www.ccsr.uiuc.edu/ucs2008/Arn..._Urbana_08.ppt

Many thanks, anticipately.

I think most of the mathematical premise of this lecture is derived from this: http://ieeexplore.ieee.org/xpl/freea...number=1686930

Oscillations in Certain Nonlinear Driven Systems
Herr, D.L.

This paper appears in: Proceedings of the IRE
Publication Date: June 1939
Volume: 27, Issue: 6
On page(s): 396- 402
ISSN: 0096-8390
Current Version Published: 2006-09-06

Abstract
The development of the theory of nonlinear oscillating systems has given rise to some rather intractable nonlinear differential equations. The formerly used isoclyne method of solution is inadequate for the solution of the equation of the nonlinear system producing relaxation oscillations under the influence of an impressed periodic force. In this paper, using the specific example of a triode oscillator with impressed sinusoidal electromotive force, differential analyzer solutions of the governing diferential equation, are given. A brief study of the phenomena of automatic synchronization and frequency demultiplication is made on the basis of the nonlinear theory.

[Ummon]

+ rep for the reference.