ANN, nonlinear dynamics, and psychoses

Omar Haneef ohaneef at andromeda.rutgers.edu
Sat Jun 27 17:16:06 EST 1998

WATTERS Paul Andrew (pwatters at mpce.mq.edu.au) wrote:
: Patrick Juola (patrick at gryphon.psych.ox.ac.uk) wrote:
: : No.  "Non-linear" does not mean "chaotic"; almost all artificial
: : networks that have been built are composed of non-linear elements
: : (as linear networks don't scale to multiple layers -- obligatory
: : reference to Minsky and Papert (1969)).

: No. Chaos _is_ non-linear. Freeman's (1987) model of the olfactory
: bulb was composed of chaotic elements which more closely
: approximated brain function than many other non-chaotic
: non-linear neural network models (IMHO).

	You know, neither of you back up what you are saying with
arguments, just non-sequiters. For instance, just because ANNs are
non-linear doesn't mean they are non-chaotic, so its irrelevant. And
just because Freeman had a nice model of the OB doesn't say anything
about the relationship between chaos and non-linearity.
	As far as I can tell, all chaotic systems are non-linear, but
not all non-linear systems are chaotic. This means there isn't an
identity relationship -- they are not the same thing -- but they are
related since non-linearity is a necessary but not sufficient
condition for chaos.
	If you add to non-linearity the absence of stable attractors,
and the presence of strange attractors in the state space, you get chaos.

: : So you need to tighten up your mathematical models (and terminology)
: : considerably.

: You need to broaden your reading considerably!

And tell me what I *need* to do!


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