🚀 go-pugleaf

Marc Lefranc (lefranc@lsh01.univ-lille1.fr) wrote:
: In <2poha4$fqa@portal.gmu.edu> [sci.nonlinear], HARRY R. ERWIN (herwin@mason1.gmu.edu) wrote:
: >I'm currently working through Abarbanel, et al., "The Analysis of
: >Observed Chaotic Data in Physical Systems," but that turns out to apply
: >to conservative systems with constant Kolmogorov-Sinai entropy, and my
: did you carefully read that paper ?

Not at the time.

: You should have a second reading: most of the material contained in that paper
: deals with dissipative systems, if not all.

but still with constant dimension.

: what does "constant Kolmogorov-Sinai" mean ?

Page 6 of the referenced paper. The Kolmogorov-Sinai entropy is the sum
of the positive Lyapunov exponents.

: constant with respect to parameters ? yes if you have a structurally stable
: invariant set, however these are generally not attractors and not the kind
: of things Abarbanel et al. consider in their paper (they are interested
: in the analysis of physical data).

My interest is in systems where there is an externally-imposed variation
in the (fractal) dimension of the attractor. This is common in
biological and social systems.

: >transients. Back in 1990, I was already wrestling with this, and in my
: >paper for the Cambridge Conference, I proposed to use topological

: interesting, which properties ?

Topological invariants.

: >properties to characterize these systems. For example, one of the key
: >concerns of peer polity elites was maintaining constant dimension, since
:                                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: again what does that mean ? dimension can only be changed by varying 
: control parameters. I know of no way to maintain a constant dimension
: when changing parameters unless you have a periodic regime

Peer polity elites typically establish population migration control
policies that prevent free movement. Huberman and his colleagues have
studied the dynamics of computational ecologies (large multi-agent
systems with time delays, errors, and local decision-making) and have
shown that these systems can show periodic and chaotic dynamics. In peer
polities, these dynamics can drive chaotic van der Pol dynamics at the
local urban sites. What you see developing is regional cooperation
between peer polity elites to prevent population movements. This
cooperation breaks down when the secular decrease of population at
individual urban sites reduces them in size to the point where they can
no longer organize their hinterlands. The system then goes into civil
war.

: >the most disruptive perturbations were those that created transient 
: >increases in the dimension of the system, so that it became chaotically 
: >uncontrollable. There are similar issues in neurodynamics.

: >Does anyone have any references to papers addressing the analysis of
: >data from systems with dissipative chaos?

: The one you quote in the beggining of your post

Yes, but there is a basic assumption that the dimension is constant...

--
Harry Erwin
Internet: herwin@gmu.edu 
Working on Katchalsky nets....