Discrete vs Continuous SD0071

[John Wolfenden]

From: John Wolfenden

I wrote:

>However, the purpose of using difference equations is that they offer a =
=3D
>tractable method of dealing with complex non-linear systems, since for =
=3D
>any dt the feedbacks in the system under review can be treated as =3D
>linear. =20

To which Joel Rahn replied:

"This is a common mis-conception. It implies that non-linear behaviour =
is=20
simply linear behaviour that has been patched together over time which =

is, of course, not true, otherwise chaotic behaviour would have been=20
discovered decades, if not a century, ago."

Ok, perhaps I have misconstrued what is happening in an SD model and/or =
been careless with my thinking. Feedback and other equations in SD =
models *can* just as easily be specified non-linear as linear, so SD =
modelling is *not* about a linear approximation of complex systems. =
Would it be more correct to say that the nature of the difference =
equations as implemented in SD is that they enable us to model a dynamic =
system via a series of static steps? That is, for each DT the *changes* =
to the state and flow variables are calculated while holding the levels =
of these variables fixed (or static), and then the flow and state =
variables are changed and the process repeated for the next DT.

I am looking for a succinct way of explaining this to colleagues in a =
way which emphasises the relative merits of the approach. It would be =
best if my characterisation was accurate ...!
_________________________________________________________________________=
__
John Wolfenden (jwolfend@metz.une.edu.au)
Centre for Water Policy Research, University of New England
Armidale NSW Australia 2351
International prefix (+61 67) Australian STD prefix (067)
Phone 732420 Fax 733237

[Jim Hines]

This responds to John Wolfendens posting # SD0086.

John wants a succinct way of stating system dynamics advantages.

John, you seem to be looking for the advantage of the system dynamics
approach in terms of the integration method. There are a number of
integration methods designed to permit a digital computer to approximate
a continuous-time simulation. The integration methods offer different
trade-offs in terms of accuracy and speed. You were describing, I
think, Euler integration.

BUT, I think the advantages you are looking for transcend the
integration method. The integration method is of considerable technical
interest. But, in terms of laying out advantages, contrasts between
integration methods pale beside the mother-of-all distinctions which is
the contrast between taking a continuous-time and discrete-time view of
the world. Continuous time modeling attempts to represent the world as
we experience it: Time keeps on flowing and things change all the time.
Discrete-time modeling (not discrete-event modeling, now) views the
world as if all decisions and all consequences occur only at evenly
separately points in time, like always on December 31st of each year.

Regards,
Jim Hines
jimhines@interserv.com

["Joel Rahn"]

On Mon, 29 Apr 1996 14:21:57 +-1000,
John Wolfenden <jwolfend@metz.une.edu.au> wrote:

>Would it be more correct to say that the nature of the difference
>equations as implemented in SD is that they enable us to model a dynamic
>system via a series of static steps?

A better phrasing, one that tries to capture the dynamic nature of SD
models (i.e., the explanation of changes over time), could be that the rate
variables tell us how fast the associated levels are changing (i.e., they
explain the changes in the levels) and that the calculation of the
variables (levels and rates) at each DT is like taking a stroboscopic
picture of the system to see where it is at each instant of evaluation.
That way, if you change DT, you change the number of times per unit of time
that you see the system, and your estimates of the rate at which the
picture is changing may be more or less precise but DT is always chosen to
give an adequate motion picture (over many observations) of the behaviour
of the system.
R. Joel Rahn
Dipartement OSD
Faculti des sciences de ladministration
Universiti Laval
Ste-Foy, Quibec
G1K 7P4 CANADA
til.: 418 656 7163 fax: 418 656 2624
e-mail: Joel.Rahn@fsa.ulaval.ca