Chaos and nonlinear dynamics

[jsterman@MIT.EDU (John Sterman)]

Bob asked us to comment on the beer game session we ran at MIT Sloan
yesterday. Jim Hines and I, with Charlie Fine (from operations
management) ran the game for the entire first year mba class. Some 220
people played (nearly 30 boards in action), and it was great. Doctoral
and second year students helped as facilitators, about 1 per 2 tables.
The game went as smoothly (maybe even more smoothly) than smaller
sessions, and the results were very typical:

Mean costs: $1950; low $537; high $4553

These costs are right in line with the results in my Management Science
paper (1989) on the beer game.

We had a great time running the game and found no diseconomies of scale
compared to the smaller sessions. And Ive also cornered the market in
Boston on red bingo chips.

John Sterman
jsterman@mit.edu

[Bob L Eberlein]

I am attaching two more replies on the chaos thread.

The discussion on chaos has been interesting and fun to read. However, I
think it is important to stress that system dynamics is not a search for chaos!
A typical pattern in mathematical modeling is to develop a mathematical model
that is shown to have certain data generating characteristics and then look to
the data to see if you can find those characteristics. This is not what is
done in system dynamics. The process of system dynamics is focussed around
having a model that is of high quality, directly interpretable and capable
of generating dynamic behavior of interest. Such models can generate chaos,
but eroding goals, oscillating morale, declining market share, spiralling
interest rates, unemployment, cost overruns, market success and urban
stagnation are also in the results.

I am looking forward to discussion on a wide variety of topics. John Sterman
and Jim Hines ran the beer game with 200 people yesterday - maybe they will
let us know how it went.

Bob Eberlein
vensim@world.std.com
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From: john@johncon.com (John Conover)
To: system-dynamics@world.std.com
Subject: Continuos sampling and discrete models

As a related issue, I have tried to use non-linear system modeling to
analyze electronic component market dynamics. I grabbed the Dept. of
Commerce numbers for electronic components, by month back to 1977, and
tried to verify that the market ups and downs were created by a
deterministic chaotic system, eg., a "strange attractor." No matter
how I tortured the data, it would not confess. I then ran the data
trough the FD3 program (hunting for fractal dimensions,) and got a
fractal dimension for the data of 0.9. No matter what I did, (cut the
data in half, use the data from every other month, cut long term
trends out with a linear fit, spline, etc.,) the fractal dimension
would not change from 0.9 (actually, all dimensions were between 0.85
and 0.92.) If I am correct, this means that the power spectrum of the
market time series was between a 1/f squared, and a 1/f cubed
distribution. This is usually characteristic of an integrative (or
cumulative,) process. But that mechanism is hard to rationalize-where
does the integrative process come from? One thing that I looked at,
was that the time series was essentially a time sampled data set, and
should have had a sin(x)/x distribution, which, although not an
integrative process, is kind of a a "low pass" filter process-but the
spectral results just didnt work out, so I still dont know where the
integrative process comes from, and am a little sceptical of the
conclusions that the time series data set was "fractal."

John

--

John Conover, 631 Lamont Ct., Campbell, CA., 95008, USA.
VOX 408.370.2688, FAX 408.379.9602
john@johncon.com
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From: "Prof. Khalid Saeed" <saeed@emailhost.ait.ac.th>
To: system-dynamics@world.std.com
Subject: Re: Stable vs. Chaotic Systems

Suggest also looking at the following references. If these cannot be
found, Ill be happy to put copies in the snail mail on request.

Saeed, K. and Bach, N. L. 1992. Chaos Out of Stiff Models. Proceedings:
System Dynamics 1992. Utrecht: System Dynamics Society

Saeed, K. and Bach, N. L. 1990. Is Deterministic Chaos Only a Property of
Models? Proceedings: System Dynamics 1990. Cambride, MA: System Dynamics
Society.

Khalid Saeed
Asian Institute of Technology
G P O Box 2754, Bangkok 10501
THAILAND