Modeling Complex Systems

Modeling Complex Systems: Graduate Texts in Contemporary Physics series, 2004, by Nino Boccara.

Review by Cosma Shalizi

How to Do It

Complex systems are those with many strongly interdependent variables. This excludes systems with only a few effective variables, the kind we meet in elementary dynamics. It also excludes systems with many independent variables; we learn how to deal with them in elementary statistical mechanics. Complexity appears where coupling is important, but doesn't freeze out most degrees of freedom.

we have had no sound introductory textbook --- one from which students would acquire more valid insights than dubious metaphysics

Happily, Boccara's new book is full of useful knowledge, and free from odd notions.

The book has three parts: two introductory chapters, three on "mean-field type models" and three on "agent-based models".

The corner-stone is chapter two, where Boccara gives a marvelous demonstration of how one models complex systems, guiding the reader through the construction of increasingly elaborate models of predator-prey oscillations in ecology, incorporating more and more sophisticated mechanisms of interaction. and testing the results against (stylized) empirical facts

The final part, on "agent-based models", delivers excellent, up-to-date chapters on cellular automata (Boccara's specialty), power-law distributions, and networks. (Readers should be aware that Boccara and computer scientists or economists define "agent-based model" in different, though ultimately equivalent, ways.) The chapter on power laws deserves special mention: it gives cautionary examples showing how easy it is to mistake other things (e.g., log-normals) for power-laws, and a prophylactic introduction to statistical hypothesis testing.

The ideal audience for this book is first- or second- year physics graduate students who have had a one-semester course in modern statistical mechanics, and so some grasp of the ideas of criticality, fluctuations, correlation functions, etc.