Order of discrete equations

[jforestr@MIT.EDU (Jay W. Forrest]

Comment on Feb. 4 email by George Richardson <GR383@ALBNYVMS.BITNET>

George comments "It has always seemed puzzling to me that the conditions
for mathematical chaos in continuous systems are more restrictive
than in discrete representations (at least three stocks, for example,
instead of just one in a difference equation)."

Perhaps I am misinterpreting this discussion, but is it possible to have
a truly first-order discrete equation? The solution interval between
computations stores information and adds the equivalent of one or more
additional degrees of "order." This is seen in a first order,
presumably continuous system-dynmics simulation when the solution
interval is too long and one gets oscillation at a period twice the
solution interval.

In the series of communications on chaos, I am puzzled by the references
to "stress" as applied to a system. What kind of stress? Are there not
many ways to stress a system? I do not detect much content in the
comments about stress; we would need an exact statement of the system
structure and a specific definition of the stress under discussion.

People have suggested that economic systems are chaotic. So far I do
not see them as such. In my work on the System Dynamics National Model,
we have sometimes seen model behavior that looks like it fits the usual
descriptions of chaos. However, I have always found that such behavior
arose from a quite unreasonable pathology in one or several equations.

Somewhat contrary to the preceding paragraph, there should be reference
here to the paper by John Stermsn:

Sterman, John D. (1988). Deterministic chaos in models of human
behavior: methodological issues and experimental results. System
Dynamics Review, 4(1-2), pp. 148-178.

Sterman shows that a simple product-ordering system has regions in
parameter space where chaotic behavior exists, and that those regions
are ones within which human decision makers may sometimes operate.

jforestr@mit.edu (Jay W. Forrester)

modeling