Stable, Unstable and Chaotic Systems

[Bob L Eberlein]

I am attaching 2 replies to the comment on Stable systems and chaos under
stress. For those who are not long time subscribers to the System
Dynamics Review the 1988 issue of this is devoted to chaos.

Bob Eberlein

Date: Wed, 01 Feb 1995 07:42 -0800 (PST)
From: rn_kickert@ccmail.pnl.gov
Subject: Re: Stable vs. Chaotic Systems

As a systems ecologist, I perceive this as a manifestation of why
plant and animal populations can go extinct, either locally
or globally, if the "right" stress and intensity is applied
to the system.
Ron Kickert, rn_kickert@pnl.gov
Battelle Pacific Northwest Lab., Richland, WA



Date: Wed, 1 Feb 1995 09:58:28 -0600
From: dkiel@utdallas.edu
Subject: Stable vs. Chaotic Systems - Linear vs. Nonlinear

Peter - in re stable vs. chaotic -


I think the issue is really one of linear systems (proportionate effects
- vs. nonlinear systems (potential for disproportionate effects)
A nonlinear system can be stable and when perturbed (externally
or internally) move to more erratic regimes.
A stable linear system will evidence predictability. A push of x
degree will lead to change of x degree.
I think the major question is " How many human
systems are stable and linear?"
As Jay W. Forrester has noted, "We live in a highly nonlinear
world" (European Journal of Operational Research, 1987,p. 104)
As Heinz Pagels wrote, prior to his death, "..life is nonlinear.
And so is everything else of interest" (The Dreams of Reason, 1988, p.56)


Doug Kiel
Associate Professor
University of Texas at Dallas
(214) 883-2019

[Bob L Eberlein]

Two more replies on Chaos . . . Bob Eberlein

Date: Wed, 1 Feb 95 14:09:10 MST
From: "Robert Levi" <dawson@usa.net>

Ilya Prigogines (nobel prize winning chemist) theory of dissapative
structures says that any system can be made to go chaotic if it exceeds its
own bounds of stability (through excess stress placed on the system), and
that if it reaches a "bifurcation point," or critical juncture in the
evolution of the system, a very, very small perturbation in a certain
direction can cause the system to transform to a new level of organization.
This is one of the bases of the "butterfly-flapping" theory.
Robert Levi | 4801 N. 107th St. | voice: 303/665-6679,x361
Director of Computing | Lafayette, CO 80026 | fax: 303/665-0757
Alexander Dawson School | email: dawson@usa.net | Systems Thinking Junkie

Date: Wed, 1 Feb 1995 16:45:09 -0500 (EST)
From: "JAMES T. HENNESSEY JR" <thenness@osf1.gmu.edu>

Peters model is very sophisticated and illustrates the role of stress on
organizations very well. I wonder if it is possible to forecast the
effects of stress on generic organizations? For example, change
literature maintains that organizations that have undergone change
recently accommodate change better as do larger organizations. Will the
model predict this for those recently experiencing change or larger, more
stable organizations?

Tom Hennessey

["Prof. Khalid Saeed"]

My experimentation with chaotic modes shows that chaotic regions consist
largely of stiff parameter sets. This means chaos shown in simulated behavior
could be attibuted to integration errors. Many models tested also showed
serious formulation errors and unreasonable parameter sets. I, nonetheless,
do not rule out the existence of chaotic modes in reality, although a
caution in experimentation which chaotic models is in order.


Khalid Saeed, AIT, GPO Bx 2754, Bangkok 10501, Thailand