Synergetics, according to E. J. Applewhite, was Fuller's name for the geometry he advanced based on the patterns of energy that he saw in nature. For Fuller, geometry was a laboratory science with the touch and feel of physical models--not rules out of a textbook. It gains its validity not from classic abstractions but from the results of individual physical experience. Description by the Buckminster Fuller Institute, courtesy of The Estate of Buckminster Fuller

Over the past years the field of synergetics has been mushrooming. An ever increasing number of scientific papers are published on the subject, and numerous conferences all over the world are devoted to it. Depending on the particular aspects of synergetics being treated, these conferences can have such varied titles as "Nonequilibrium Nonlinear Statistical Physics," "Self-Organization," "Chaos and Order," and others. Many professors and students have expressed the view that the present book provides a good introduction to this new field. This is also reflected by the fact that it has been translated into Russian, Japanese, Chinese, German, and other languages, and that the second edition has also sold out. I am taking the third edition as an opportunity to cover some important recent developments and to make the book still more readable. First, I have largely revised the section on self-organization in continuously extended media and entirely rewritten the section on the Benard instability. Sec ond, because the methods of synergetics are penetrating such fields as eco nomics, I have included an economic model on the transition from full employ ment to underemployment in which I use the concept of nonequilibrium phase transitions developed elsewhere in the book. Third, because a great many papers are currently devoted to the fascinating problem of chaotic motion, I have added a section on discrete maps. These maps are widely used in such problems, and can reveal period-doubling bifurcations, intermittency, and chaos.

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 formation 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 mathematics: Elaborate formal proofs and rigorous estimates are often replaced in 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.

For centuries, humankind has believed that the world with all its form and structure was created by supernatural forces. In recent decades science has shaken these beliefs with the discovery of the exciting possibility of a self-created and self-creating world ? of self-organization. Synergetics endeavours to reveal the intimate mechanisms of self-organization. The transitions from chaos to order, the nature of self-organization, the various approaches to it and certain philosophical inferences are outlined. Synergetics thus represents a remarkable confluence of many strands of thought, and has become a paradigm in modern culture. This book exposes the reader to striking new vistas in physics and mathematics, chemistry and biology, social sciences and philosophy ? all interlocked around the concept of self-organization.

This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.

The publication of this second edition was motivated by several facts. First of all, the first edition had been sold out in less than one year. It had found excellent critics and enthusiastic responses from professors and students welcoming this new interdisciplinary approach. This appreciation is reflected by the fact that the book is presently translated into Russian and Japanese also. I have used this opportunity to include some of the most interesting recent developments. Therefore I have added a whole new chapter on the fascinating and rapidly growing field of chaos dealing with irregular motion caused by deterministic forces. This kind of phenomenon is presently found in quite diverse fields ranging from physics to biology. Furthermore I have included a section on the analytical treatment of a morphogenetic model using the order parameter concept developed in this book. Among the further additions, there is now a complete description of the onset of ultrashort laser pulses. It goes without· saying that the few minor mis prints or errors of the first edition have been corrected. I wish to thank all who have helped me to incorporate these additions.

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This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.

The spontaneous formation of well organized structures out of germs or even out of chaos is one of the most fascinating phenomena and most challenging problems scientists are confronted with. Such phenomena are an experience of our daily life when we observe the growth of plants and animals. Thinking of much larger time scales, scientists are led into the problems of evolution, and, ultimately, of the origin of living matter. When we try to explain or understand in some sense these extremely complex biological phenomena it is a natural question, whether pro cesses of self-organization may be found in much simpler systems of the un animated world. In recent years it has become more and more evident that there exist numerous examples in physical and chemical systems where well organized spatial, temporal, or spatio-temporal structures arise out of chaotic states. Furthermore, as in living of these systems can be maintained only by a flux of organisms, the functioning energy (and matter) through them. In contrast to man-made machines, which are to exhibit special structures and functionings, these structures develop spon devised It came as a surprise to many scientists that taneously-they are self-organizing. numerous such systems show striking similarities in their behavior when passing from the disordered to the ordered state. This strongly indicates that the function of such systems obeys the same basic principles. In our book we wish to explain ing such basic principles and underlying conceptions and to present the mathematical tools to cope with them.