Discrete vs Continuous SD0071
Posted: Mon Apr 29, 1996 2:21 pm
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
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