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Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences

Frank Schweitzer

posted on 19 December 2003

reviewed by Enrico Scalas

The field discussed by the book of Frank Schweitzer has been recently popularized by a novel of Michael Crichton: "Prey". If you want to know more about flocks and swarms and you are interested not only in science fiction, but also in science, the work of Frank Schweitzer is the right place to start with. The popularization of a rather esoteric scientific field, as the one discussed by Schweitzer, is a clear sign of its increasing relevance.

As usual, Crichton's book has a list of references and, as usual, almost only research performed in the United States is quoted. You will find many clues on this US tendency to completely overlook the work done elsewhere in the world also in the book of Schweitzer. Schweitzer's bibliography does justice to the huge efforts taking place in Germany and in Europe. Even if it is very difficult to give proper credits dealing with such a large range of issues as Schweitzer does, his bibliography is to be praised. His book is about Brownian agents, a smart generalization of Brownian particles including internal states. Brownian agents can be effectively used as phenomenological models for many natural and social phenomena including track formation in biological systems, movement and trail formation of humans, evolutionary optimization strategies, urban growth, quantitative sociodynamics, spatial opinion structures in social systems.

Schweitzer's approach is gradual. The first four chapters are devoted to introducing more and more complexities and subtleties in the Brownian agent models, and the focus is on the models themselves rather than on the systems. Reading and understanding these chapters may be a difficult time-consuming task, but the reward is high. Starting from chapter five (on tracks and trail formation in biological systems) and ending with chapter ten (on opinion formation), the reader can amuse him/herself in dealing with models of real systems and devote his/her attention to the more relevant issues for his/her research.

This book contains some gems. My favorite one is in chapter nine: the discussion of a spatial dynamic model for the labor market introduced by the well-known US economist Paul Krugman where "workers are assumed to move toward locations that offer them higher real wages". Schweitzer shows not only that Krugman's model is nothing else that an instance of a selection equation of the Fisher-Eigen type, but also, using the formalism developed previously, he can easily generalize it and question the economic meaning of the assumptions leading to Krugman's equations.

A limit of this book is that the comparison between theoretical results and available empirical data is not always discussed. In many cases, however, not many empirical data are available or of good quality. In this respect, this book can become a stimulus for further empirical research in the fields outlined.

Finally, as in many contemporary books, there are various misprints scattered throughout the chapters. However, these are minor and do not hamper the understanding of the text.

I can recommend this book to all those working in the field of complex systems. They will find a detailed survey of the Brownian agent method and they might get good hints for further research in some of the fascinating fields herein discussed.