There's a mathematical chemotaxis model

~~for slime molds~~ that I've always found interesting in terms of the dynamics: the solutions can decay from chaotic into both periodic and homogenous.

http://www.sciencedirect.com/science...67278910002617
Spatio-temporal chaos in a chemotaxis model

Kevin J. Paintera, Thomas Hillenb

Physica D: Nonlinear Phenomena

Volume 240, Issues 4–5, 15 February 2011, Pages 363–375

~I guess it's supposed to be a more general chemotaxis model. Not sure why I equated it to slime molds in my memory, maybe the behavior of aggregating cell bodies?

~~ok, it does mention slime molds, just by latin name!