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.
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!