I'm not really clear what you are trying to do with these models, but agent based modeling may be related : http://en.wikipedia.org/wiki/Agent-based_model http:

I'm not really clear what you are trying to do with these models, but agent based modeling may be related : http://en.wikipedia.org/wiki/Agent-based_model http://en.wikipedia.org/wiki/Agent-based_model This may be a useless comment, but I would also recommend you focus on the software engineering aspect - provide a clean, simple interface that describes what you want and do a naive implementation that will allow you to work out the rest of your system, then you can keep working while studying the ideal mathematical model for behavior. I think the general search term for this field is "numerical analysis". One quick and dirty technique that is sometimes useful if you have a set of input vectors and a set of goal states is to do polynomial interpolation with something like a lagrange polynomial.