A round-up of some relevant papers on this subject, with an emphasis on those utilising reaction-diffusion and related systems:
- Neurocomputation by Reaction Diffusion, by Ping Liang in Physical Review Letters (1995)
This is the closest I’ve found to the approach taken by Lesser et al in modelling the mind/brain, mathematically speaking. Explores seriously the computational possibilities of diffusion-based (non-syaptic) mechanisms, which is still quite uncommon in neural modelling. Very interesting work, although there seems to have been surprisingly little direct follow-up. However, see also:
- Neural information processing using network-in-a-field by Ping Liang in Neural Networks, 1996., IEEE International Conference on
Which explores coupling between synaptic and diffusive information transmission, as does
- Flexible Couplings: Diffusing Neuromodulators and Adaptive Robotics by Andy Philippides, Phil Husbands, Tom Smith and Michael O’Shea in Artificial Life 11: 139–160 (2005)
This goes into the role of nitric oxide as a neurotransmitter, and the possibilities of models inspired by its action in an evolutionary robotics setting.
- Modeling Complex Systems by Reaction-Diffusion Cellular Nonlinear Networks with Polynomial Weight-Functions by Frank Gollas and Robert Tetzlaff
This is related to Ping Liang’s work, as above, and probably worth exploring. The same authors have also worked on modelling and predicting epileptic seizures using R-D systems, an intriguing possibility, but I so far haven’t been able to download that paper.
- Dynamical approaches to cognitive science, by Randall Beer
Discusses three examples of dynamical systems in cognitive science, with some dicussion of the merits of this approach over other strategies of cognitive modelling. A very useful review.
- The dynamical systems approach to cognition by Wolfgang Tschacher and Jean-Pierre Dauwalder (eds) (2003)
The introduction is available for download at the above page, and substantial portions of the book are available on Google Books – however, I look forward to seeing the book itself, which I will have to get on inter-library loan.
- On What Makes Certain Dynamical Systems Cognitive: A Minimally Cognitive Organization Program by Xabier Barandiaran in Adaptive Behavior, Vol. 14, No. 2, 171-185 (2006)
An interesting piece about how one might make a convincing case for the cognitive properties of a dynamical system.
- The dynamical hypothesis in cognitive science by Tim van Gelder in Behavioral and Brain Sciences (1998), 21: 615-628 Cambridge University Press
Van Gelder has evidently been a major player in pushing the idea that a dynamical systems approach to understanding cognition could be fruitful. He is referenced widely, though some aspects of his work have come in for substantial criticism.