chaos in models of neuronal excitabillity

Kevin Spencer kspencer at iti.org
Wed Sep 28 15:39:02 EST 1994

ak426 at FreeNet.Carleton.CA (Daniel Racicot) writes:

>I have recently been looking over some material on neuronal excitabillity.
>For the most part I have concentrated on the Hodgkin Huxley model and the 
>Fitzhugh Nagumo model as well as Plant's slow wave burster model.  It would
>seem to me that these equations are capable of "chaotic" motion.  
>I would be interested in hearing about any articles where such claims
>have been made.  
>I seem to recall seeing a few articles where the claim is that they
>have calculated something which would indicate chaos in the experimental
>data (eg they have calculated a positive largest lyapunov exponent)
>but so far (and it has been a short search) I have not seen
>any useful claims at observing chaos in the HH equations for example.

>Has anyone actually done some bifurcation analysis or some kind of 
>parameter search on these equations to see if there is anything 
>interesting there?  

I read a paper several years ago by Aihara et al. (I think this is the
name) in a physics journal.  If my memory is correct, the authors looked
at the dynamics of the H-H model and did do bifurcation analysis.  They
also did something with deriving back-propagation (now my memory is really
fuzzy).  At the time I read the paper I didn't know anything about the
H-H model and dynamical systems, so it was over my head.  Got to go find
it now...

Kevin Spencer
Cognitive Psychophysiology Laboratory and Beckman Institute
University of Illinois at Urbana-Champaign
kspencer at p300.cpl.uiuc.edu / kspencer at psych.uiuc.edu

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