Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Well, this is exactly the sort of modeling question many students (and professors) bring to our yearly summer program in NKS. I can point you to some examples, but to come up with the right model for your particular system requires some ongoing interaction to flesh out details.
For an example of modeling a natural system with a CA in an ecology context, you might look for this article in the latest Complex Systems -
Brian Beckage, Chris Ellingwood
Fire Feedbacks with Vegetation and Alternative Stable States
Positive feedbacks between vegetation and fire disturbance may lead to nonlinear ecosystem responses to variation in fire regime. We used a cellular automaton model of fire–vegetation dynamics based on pine savanna communities to explore the potential for fire–vegetation feedbacks to lead to ecological thresholds and abrupt transitions between alternate ecosystem states. We show that (i) ecosystems can rapidly move between grassland and forest states in response to gradual changes in fire regimes or initial landscape composition and that (ii) hurricane disturbances can mediate the frequency of fire that leads to ecological thresholds. Nonlinear ecosystem dynamics lead to sensitivity to initial conditions and bistable ecological communities that can exist in either a grassland or forest state under the same disturbance frequency. Our results indicate that gradual changes in global climate that influence disturbance frequency may result in the rapid transformation of landscapes through feedbacks between fire and vegetation.
Beckage has already done some modeling work in this issue, when he attended NKS 2007 at the University of Vermon (where he teaches, incidentally). We worked on implementing an improved version of his ideas in Mathematica, and that model was his project, and became the basis of this paper.
As for examples of NKS models of urban growth processes, we had a student the previous year, Igor Lugo, whose project focused on that. But it was less of an empirical study, more a search for a minimalist model of an urban growth process.
For a monograph directly in the area you are interested in, you might look for the following book by Michael Batty -
I hope this helps.
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