Foundations of Synergetics

This is an introduction to the mathematical theory of co-operative behaviour in active systems of various origins, both natural and artificial. The first of two volumes, it concentrates on the properties of regular self-organized patterns in distributive active systems.

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This textbook presents an introduction to the mathematical theory of cooperative behaviour in active systems of various origins, both natural and artificial. This volume (the first of two) is devoted to the properties of regular self-organized patterns in distributed active systems. An analysis of pattern formation and self-supported wave propagation in active media is followed by a description of the properties of neural networks and their possible applications in the field of distributed analog information processing. The volume ends with a discussion of reproductive networks and evolutionary systems. Attention is focused on basic models which might appear in a wide range of applications. As illustrations, the author uses simplified examples borrowed from a variety of disciplines ranging from chemical and biological physics to market economics. The new edition has been thoroughly revised and updated to incorporate recent advances in this exciting field.