RE: Simulating Individual Behavior

[Theodore C. Belding]

Hi Scott-

At 9:23 PM -0700 4/18/97, Scott Christley wrote:
>I am tending to notice a separation between two modelling paradigms: the
>ABMers (I was an IBMer once! ;-) and the ODEers.  Are there true
>differences between these two paradigms or is it only a perception?
>Meaning is not a Swarm program a symbolic (mathematical) description of a
>model, just not as concise as a differential equation?

Using ODEs to model an agent-based model like Conway's Game of Life may be
theoretically possible, but it's often a very bad representation.  It's
like using a Fourier series of sine waves to represent a square (pulse)
waveform.  The Fourier series representation needs a huge number of terms
to even approach the accuracy that another type of representation would
have (say step functions).  On the other hand, using step functions to
represent a sine wave is not the best representation.  Doyne Farmer and
Norman Packard, as well as John Holland, have written about the need for
using an appropriate, efficient representation of a dynamical system.  For
something like the Game of Life, I think the most appropriate
representation is in term of agents, not ODEs.

If we agree that in some cases we want to use ODEs and in others we want to
use agent-based models to model a system, then I think we also have to
recognize that each modeling paradigm has different tools that are needed
to work with them.  A lot can be determined about ODEs using traditional
mathematical techniques, as well as numerical simulation techniques.   In
agent-based models we don't have many mathematical tools at present and
usually must rely much more on computer simulation of the agents' behavior.
Using ODE tools to analyze an agent-based model (or vice-versa) is like
using a hammer to pound a screw in.  In this sense, an agent-based model is
very different from an ODE, even though they're both mathematical
formulations at some level.
-Ted

--
Ted Belding                      <mailto:address@hidden>
University of Michigan Program for the Study of Complex Systems
<http://www-personal.engin.umich.edu/~streak/>




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