Posted by
Bruce Sawhill on
Dec 31, 2003; 12:06pm
URL: http://friam.383.s1.nabble.com/The-Importance-of-Being-Discrete-Life-Always-Wins-on-the-Surface-tp519040p519041.html
There are several famous examples where discreteness gives a completely
different result than continuity:
1. Period doubling route to chaos (discrete iteration of logistic
equation x[i+1]=r x[i](1-x[i]). Continuity (integrating differential
equation) gives S-curve to saturation.
2. Kimura's results on genetic drift. (start with 50% of each of two
competing alleles, one always excludes the other eventually)
Continuity says 50% stays 50%.
Cheers,
Bruce
On Wednesday, December 31, 2003, at 08:33 AM, Owen Densmore wrote:
> Someone on the NetLogo list sent a reference to this:
>
http://arxiv.org/abs/adap-org/9912005> .. saying:
> I was fascinated a few years ago to read Shnerb's PNAS article on
> "The
> Importance of Being Discrete," exhibiting qualitatively different
> behaviors
> in an equation-based and an entity-based model of the same system ...
>
> Owen Densmore 908 Camino Santander Santa Fe, NM 87505
>
[hidden email] Cell: 505-570-0168 Home: 505-988-3787
> AIM:owendensmore
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