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Using simple models this book shows how we can gain insights into the behavior of complex systems. It is devoted to the discussion of functional self-organization in large populations of interacting active elements. The authors have chosen a series of models from physics, biochemistry, biology, sociology and economics, and systematically discuss their general properties. The book addresses researchers and graduate students in a variety of disciplines.

This book, written by two well-known scientists, represents an excellent ad­ dition to the Springer Series in Synergetics in several ways. It shows how by rather simple models we can gain remarkable insights into the behavior of complex systems. At the same time it demonstrates the progress made in this interdisciplinary field. While in the early days of Synergetics, the self­ organized coherent action of atoms in the laser - a physical device - was in the foreground of interest (cf. my book Synergetics: An Introduction (Springer, Berlin, Heidelberg, New York 1977)), the coherent action of nerve cells got into the focus of research, as is witnessed by the book by P. Tass in this series (P. Tass, Phase Resetting in Medicine and Biology (Springer, Berlin, Heidel­ berg, New York 1999)). In these books the elements were disturbed by noise. Now, in the present book by Mikhailov and Calenbuhr, the self-organized coherent action of otherwise chaotic elements is studied and important as well as surprising results by Kaneko, Mikhailov and others are presented. Let me mention just another highly interesting problem treated in this book: the coherent interaction of tens of thousands of reactions going on in biological cells. But other phenomena, such as the formation of swarms of fish or the collective behavior of ants, are also modelled. These are just a few examples of the many fascinating subjects dealt with in this book that relate to many disciplines under unifying aspects.

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This book shows how, by rather simple models, we can gain remarkable insights into the behavior of complex systems. It is devoted to the discussion of functional self-organization in large populations of interacting active elements. The possible forms of self-organization in such systems range from coherent collective motions in the physical coordinate space to the mutual synchronization of internal dynamics, the development of coherently operating groups, the rise of hierarchical structures, and the emergence of dynamical networks. Such processes play an important role in biological and social phenomena. The authors have chosen a series of models from physics, biochemistry, biology, sociology and economics, and will systematically discuss their general properties. The book addresses researchers and graduate students in a variety of disciplines, such as physics, chemistry, biology and the social sciences.

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1. Introduction.- 2. The Games of Life.- 3. Active Motion.- 4. Ridden by the Noise ....- 5. Dynamics with Delays and Expectations.- 6. Mutual Synchronization.- 7. Dynamical Clustering..- 8. Hierarchical Organization.- 9. Dynamics and Evolution of Networks..- References.

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