The emergence of complex behavior in a system consisting of interacting elements is among the most fascinating phenomena of our world. Examples can be found in almost every field of today's scientific interest, ranging from coherent pattern formation in physical and chemical systems, to the motion of swarms of animals in biology and the behavior of social groups. The question of how the system properties on the macroscopic level depend on the microscopic interactions, is one of the major challenges in complex systems and, despite a number of different attempts, by now far from being solved.
In order to gain insight into the interplay between microscopic interactions and macroscopic features, it is important to find a level of description that on the one hand considers specific features of the system and is suitable to reflect the origination of new qualities, but on the other hand is not flooded with microscopic details. In this respect, agent models have become a very promising tool mainly for simulating complex systems. A commonly accepted theory of agent systems that also allows analytical investigations is however still pending because of the diversity of the various models invented for particular applications. It will be a multi-disciplinary challenge to improve this situation, in which also statistical physics needs to play its part, both by contributing concepts and formal methods.
The present book wants to contribute to this development. Firstly, we introduce a particular class of agent models denoted as Brownian agents and show its applicability to a variety of problems ranging from physico-chemistry to biology to economy and the social sciences. As we will demonstrate, the Brownian agent approach provides a stable and efficient method for computer simulations of large ensembles of agents. Secondly, we do not just want to present simulation results, but also want to use the methods of statistical physics to analyze the dynamics and the properties of systems with large numbers of Brownian agents, this way contributing pieces for a formal approach to multi-agent systems.
Similar to Brownian particles, Brownian agents are subject to both deterministic and stochastic influences, which will allow us to derive a generalized Langevin dynamics for their activities. Different from physical particles, however, Brownian agents have individual degrees of freedom that allow them to respond differently to external signals, to interact with other agents, to change their environment or to perform active motion. Because all kind of activities need energy, an important internal degree of freedom is the agent's energy depot. In this book, we will extensively investigate the influence of the internal energy depot on the active, self-driven motion of the agents that in this respect are denoted as active particles. But also other activities, such as the interaction via an adaptive ``landscape'' - a field generated by the agents that feeds back to their further behavior - will be widely discussed.
Because of the many examples from very different application areas, the book will be of interests not only for physicists interested in self-driven motion or physico-chemical structure formation, but also for biologists who want to model the collective behavior of bacteria or insect societies, or for engineers looking for effective algorithms for the self-assembling and optimization of networks. Major parts of the book are also devoted Brownian agent models in social, urban and economic problems, to inspire scientists from these fields to apply the concept. Among the examples are models for urban and economic agglomeration, but also models of human behavior, such as the motion of pedestrians or the formation of collective opinions. The book will show that within the framework provided by statistical physics, non-linear dynamics and the theory of stochastic processes, a formal description of Brownian multi-agent systems can be achieved, which also allows to derive critical parameters to be used for the computer simulations, and to predict the outcome of a collective dynamics.
The investigations presented in this book have been carried out in the years of 1992 to 2001 mainly at the Institute of Physics at Humboldt University Berlin in close collaboration with the Sonderforschungsbereich (SFB) 230 ``Natural Constructions'' (Stuttgart) (1992-1995), further at the Department of Physics at Emory University, Atlanta, GA (1993) and the Department of City and Regional Planning at Cornell University, Ithaca, NY (1997). A new light was shed on the results obtained during these years, when I started to work at the GMD Institute for Autonomous Intelligent Systems (now part of the Fraunhofer Society) in Sankt Augustin in 1999. The challenge to combine concepts from distributed artificial intelligence and new simulation methods for multi-agent systems with the approaches of many-particle physics eventually gave this book a new direction.
I want to express my sincere thanks to Werner Ebeling (Berlin) whose fundamental work on the physics of self-organization and evolution in complex systems is one of the methodological bases of my investigations. He was actively involved in developing the ideas of active Brownian particles. Over the years, he promoted my interdisciplinary engagement, which could thrive in the broad-minded scientific atmosphere of his research group. Further, I am very indebted to Lutz Schimansky-Geier (Berlin). Many of the ideas about interacting Brownian particles presented in this book were developed in close collaboration with him. His suggestions and critical remarks always gave new impulses for improving and extending the concept. Eventually, I would like to thank Heinz Mühlenbein (Sankt Augustin) for his enduring support of my work and for very many stimulating discussions in a superb working atmosphere.
For collaboration, for discussions, suggestions, critical remarks, for various forms of encouragement, for invitations and support, I would like to thank further (in alphabetical order) Wolfgang Alt (Bonn), Torsten Asselmeyer (Berlin), Jörn Bartels (Rostock), Vera Calenbuhr (Brussels), Andreas Deutsch (Bonn), Jean-Louis Deneubourg (Brussels), Feredoon Family (Atlanta), Hermann Haken (Stuttgart), Dirk Helbing (Stuttgart), Janusz Holyst (Warsaw), Klaus Humpert (Stuttgart), Peter Fleissner (Vienna), Jan Freund (Berlin), Hans-Jürgen Krug (Berlin), Lui Lam (San Jose), Kenneth Lao (Atlanta), José Lobo (Ithaca), Thilo Mahnig (Sankt Augustin), Péter Molnár (Atlanta), Ludwig Pohlmann (Berlin), Steen Rasmussen (Los Alamos), Gernot Richter (Sankt Augustin), Rupert Riedl (Altenberg), Gerd Röpke (Rostock), Helge Rosé (Berlin), Andrea Scharnhorst (Berlin), Eda Schaur (Innsbruck), Hans-Joachim Schellnhuber (Potsdam), Richard Schuler (Ithaca), Gerald Silverberg (Maastricht), Jens Steinbrink (Berlin), Angela Stevens (Heidelberg), Benno Tilch (Stuttgart), Rüdiger Wehner (Zurich), Wolfgang Weidlich (Stuttgart), Olaf Weiss (Berlin), Jörg Zimmermann (Bonn) and all colleagues and friends not mentioned here.
This work was made possible by two personal grants from the Deutscher Akademischer Austauschdienst (DAAD) (1993) and the Deutsche Forschungsgemeinschaft (DFG) (1996-1998) which I would like to thank very much for their financial support.
Indispensable, and yet free of charge were the tools for completing this book, namely LATEX, the GNU Emacs, and the LINUX operating system with its various useful applications. So, I finally want to express my thanks to all the developers and maintainers of these wonderful programs.
Sankt Augustin and Berlin
Frank Schweitzer