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The Importance of Being Discrete - Life Always Wins on the Surface

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
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