There are two simple linear models, given as examples in the classical book of Luenberger [1]: the arms race model by Richardson [2] and the Homans-Simon model group interaction [3,4,5]. Please, see [1] to a more detailed explanation. These are two examples of the so-called positive linear systems.
1. David G. Luenberger: Introduction to Dynamic Systems, Theory, Models, and Applications. New York: John Wiley & Sons, 1979, 446 pp
2. Lewis Fry Richardson: Arms And Insecurity: A Mathematical Study Of The Causes And Origins Of War. Chicago: Pittsburgh Quadrangel Book, 1960
3. G.C. Homans: The Humen Group. New York: Harcourt Brace Jovanovich, 1950
4. H.A. Simon: Models of Man. New York: Wiley, 1957.
5. I. W. Sandberg, "On the Mathematical Theory of Interaction in Social Groups," in IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-4, no. 5, pp. 432-445, Sept. 1974.
I had in mind the same book by David Luenberger that Prof. José Mario Araújo has mentioned.
The book has a whole bunch of good articles and has many mathematical developments.
Good luck with this interesting research.
Prof. A. Rodolfo S. Carrara, Ph.D. - Univ. Federal do Rio Grande do Sul / Mech. Eng. Dept. / Research Group on Design, Industrial Automation and Manufacturing - porto Alegre - RS - Brazil.
I was surprised to see that all the recommendations so far date back 50 years or so! A great deal is going on right now involving complex social dynamical systems notably employing agent based modelling. Try scanning back issues of the free online journal JASSS (Journal of Artificial Societies and Social Simulation). Many interesting applications there. You might also like to glance at my own (wildly ambitious but hopefully thought provoking and in principle feasible!) MoHAT project here on RG.
Today I found a new publication in Annual Reviews in Control. Do do not have an access to full text, but summary sounds promising: http://www.sciencedirect.com/science/article/pii/S1367578817300172