This book gives an introduction to the mathematical theory of
cooperative behavior in active systems of various origins, both natural
and artificial. It is based on a lecture course in synergetics which I
held for almost ten years at the University of Moscow. The first volume
deals mainly with the problems of pattern fonnation and the properties
of self-organized regular patterns in distributed active systems. It
also contains a discussion of distributed analog information processing
which is based on the cooperative dynamics of active systems. The second
volume is devoted to the stochastic aspects of self-organization and the
properties of self-established chaos. I have tried to avoid delving into
particular applications. The primary intention is to present general
mathematical models that describe the principal kinds of coopera- tive
behavior in distributed active systems. Simple examples, ranging from
chemical physics to economics, serve only as illustrations of the
typical context in which a particular model can apply. The manner of
exposition is more in the tradition of theoretical physics than of in
mathematics: Elaborate fonnal proofs and rigorous estimates are often
replaced the text by arguments based on an intuitive understanding of
the relevant models. Because of the interdisciplinary nature of this
book, its readers might well come from very diverse fields of endeavor.
It was therefore desirable to minimize the re- quired preliminary
knowledge. Generally, a standard university course in differential
calculus and linear algebra is sufficient.
