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 selforganized 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 selforganization and the properties of selfestablished 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.

This book is devoted to Large Scale Systems methodologies including decomposition, aggregation, and model reduction techniques. The focus is put on theoretical and practical results resulting from the application of these techniques in the area of stability and decentralized control. Every result is illustrated by examples to facilitate understanding. The appendices provide a collection of readytouse packages implementing some algorithms included in the book. Graduate students concerned with system and control theory will be interested in this book, since it offers a global synthesis on the problem of structurally constrained control. The book addresses also scientists and lecturers in the areas of large scale systems and control theory.

This book contains the invited papers of an international symposium on synergetics; which was held at Schlol3 Elmau, Bavaria, FRG, April 27 to May 1, 1981. At our previous meetings on synergetics the selforganized formation of structures in quite different disciplines stood in the foreground of our interest. More recently it has turned out that phenomena characterized by the word "chaos" appear in various disciplines, and again farreaching analogies in the behavior of quite different systems become visible. Therefore this meeting was devoted not only to problems connected with the occurrence of ordered structures but also to most recent results obtained in the study of chaotic motion. In the strict mathematical sense we are dealing here with deterministic chaos, i. e. , irregular motion described by deter ministic equations. While in this relatively young fieJd of research computer ex periments and computer simulations predominated in the past, there now seems to be a change of trend, namely to study certain regular features of chaos by analytical metbods. I think considerable progress has been achieved in this respect quite recently. This theoretical work is paralleled by a number of very beautiful experi ments in different fields, e. g. , fluid dynamics, solidstate physics, and chemistry. For the first time at this kind of meeting we have included plasma physics, which presents a number of most fascinating problems with respect to instabilities, formation of structures, and related phenomena.

This book introduces a new set of practical principles for eliminating and reducing risk in any kind of system, whether financial or non financial and including engineering, computer and business systems  and even military systems. Although these new principle have come from research into risk in engineering and computer systems, surprisingly, they also resolve an old dispute in the investment arena, between the academic theorists who use the beta measure of risk and the followers of the ideas of the late Benjamin Graham, and his famous disciple, Warren Buffett. Each side is well known for castigating the theories and ideas of the other, with seemingly little common ground. The new risk principles, and principles for eliminating risk, show clearly that both sides in this famous dispute are right, for the new principles bridge the gap between the two. They show that the betatheory proponents simply had failed to develop their theory far enough  their risk measure in particular  to include risk elimination possibilities. At the heart of the new theory of risk in systems are two ideas: first, the idea of extending the risk measure to include average system output loss with respect to the bestcase system output, and second, the idea of eliminating those output losses with respect to the best case, thus preserving the benefit of running the risk. The author presents the new principles along with many practical and numerical examples, and the essential ideas are clearly explained. Nevertheless, if you examine the material closely, you will find that it will withstand a rigorous analysis. There are some elementary mathematical relationships in the book, but because their meaning is also well explained in words, and reinforced by practical examples, these can often be skipped. The intent is to enable you to grasp the ideas and concepts well enough to enable you to put them to practical use, in whatever your field of endeavor, anything from spacecraft engineering, to computer systems design, to investment management.
