[Hajman]

However, randomly generated mutations do act like diffusion. There are no "charastics" for diffusion equations. Things happen at all scales.

That's one reason I pinged you. I think I need better books (have Nonlinear Dynamics and Chaos and a number of others, but they don't mention that diffusion is necessary for chaotic boundries. I don't think it mentions diffusion period, at least not in name, though I could be missing a concept somewhere. Any suggestions for a more in-depth reference?). How would that affect the dynamics of the random mutation system? Or more specifically, what would be required to gain a possible chaotic boundry like a cusp catastrophe? (The book mentioned gives examples of biological growth such as insect outbreaks as cusp catastrophic effects).

-The Hajman-

[Doctor Stochastic]

I don't know of any. I just (on my own, thus no publication because no funding, and I don't have to prove anything) developed the idea of using a (high dimensional) random walk to simulate mutation and some sort of selection for culling. I was surprised that the culling (natural or human selection) seemed to make things converge really fast (probably exponentially fast). This is useful in genetic algorithms.

You might look at the litterature on "particle filters." Not the dust stuff, the "control of electrical signals" stuff.

Chaos isn't really diffusion. It operates somewhat differently. There's no reason that one couldn't have both though.

[WildTurkey]

That's one reason I pinged you. I think I need better books (have Nonlinear Dynamics and Chaos and a number of others, but they don't mention that diffusion is necessary for chaotic boundries. I don't think it mentions diffusion period, at least not in name, though I could be missing a concept somewhere.

Diffusion is a first order approximation to the more accurate transport theory and applies for mono-energetic applications only.