Re: ABM/I(C?)BM

[Mark P. Line]

Steve Emsley wrote:
> 
> One posting suggested that ODEs are attractive due to the possibility
> of their analytical solution.

I don't remember anybody saying that, although I wrote that ODE's were
invented in order to provide analytical solubility for otherwise
intractable problems.

I also wrote that no interesting problem formulated as ODE's or PDE's is
likely to be analytically soluble, and that therefore their rationale as
tools for analytical manipulation no longer exists. 

In saying that, I was trying to imply that, if we're going to have to 
attack our models numerically anyway, then we might as well go straight
for an ABM representation instead of blissfully accepting the
inappropriate assumptions (e.g. differentiability) of ODE's and PDE's.
Those assumptions were the lesser evil when the problem at hand was
otherwise intractable, period. That's no longer the case in domains
where we can build useful ABM's.


> IMHO if you have an ODE-based ecology
> capable of analytical solution (rather than numerical simulation) you are
> dealing with a mathematical abstraction (ecology as an excitable medium)
> NOT a system that propagates through time based on local interactions and
> continually varying stochastic or adaptive parameters i.e. a real
> ecosystem.

Precisely. It is unlikely that a useful [OP]DE model of an observed
system will be capable of analytical solution.


-- Mark

(Mark P. Line  --  Bellevue, Washington  --  <address@hidden>)



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