Foundations of Synergetics I
Foundations of Synergetics I

Author: Alexander S. Mikhailov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 198

ISBN-13: 3642785565

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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.

Synergetics of the Brain
Synergetics of the Brain

Author: E. Basar

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 382

ISBN-13: 3642694217

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Synergetics may be considered as an interdisciplinary effort dealing with the gene ral problem of how science can cope with complex systems. The preceding symposia on synergetics were devoted to systems of physics, chemistry and partly also biolo gy and sociology. It was possible to develop adequate concepts to describe and even to calculate evolving macroscopic spatial, temporal, and functional structures which emerge through self-organization of the individual parts of the systems under con sideration. This book contains the invited papers presented at the Symposium on the Synerge tics of the brain, Schloss Elmau, Bavaria, May 2 to 7, 1983. The inclusion of this topic in the synergetics enterprise represents a big step towards a treatment of complex systems. Most probably the human brain is the most complex system we know of. As the organizers believe, this symposium provides the reader with a good cross section of experimental results and theoretical approaches to cope with the complex problems of structure and function of the brain. It was generally felt that such a joint meeting between experimentalists and theoreticians is of great importance for future development of this field. Modern experimental methods, e. g. multielectrode derivations allow or will allow us, in short, to collect huge amounts of data. Simi larly high-speed computers will flood us with an enormous number of outputs once the basic model equations have been chosen.

Synergetics
Synergetics

Author: Hermann Haken

Publisher: Springer Science & Business Media

Published: 2004-01-12

Total Pages: 796

ISBN-13: 9783540408246

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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.

Temporal Order
Temporal Order

Author: L. Rensing

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 336

ISBN-13: 3642703321

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This volume contains the lectures and contributions presented at the International Symposium on Temporal Order held in Bremen, September 17-22, 1984. Temporal order, such as a more or less regularly repeated temporal sequence of events, can evol ve in open systems far removed from equi 1 i bri um. Progress duri ng the last decade in the analysis and the modelling of this complex phenomenon in both biological and chemical systems gave rise to the idea of a joint conference. The purpose of the symposium was to stimulate future work by enhancing the exchange of experimental and theoretical results between neighbouring disciplines. Theoretical work in general, and mathematical models in particular, provided the basis for a mutual discussion and, thus, helped to overcome difficulties in under standing the results of different experimental fields. Chemical systems, for examp le, are more rigorously controllable through their experimental conditions in com parison to biological systems, which maintain highly effective autonomous control against environmental influences. Therefore, different states such as bistability, oscillations and chaos can be defined and, hence, described better in chemical sy stems. Chemical systems may thus provide some insights into functional structures that also exist in more complex biological systems.

Lasers and Synergetics
Lasers and Synergetics

Author: Robert Graham

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 277

ISBN-13: 3642727581

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Lasers and Synergetics, written to honour Hermann Haken on his 60th birthday, is concerned with the two main areas of research to which Prof. Haken has made fundamental contributions. In fact, the two areas are interrelated since the development of the interdisciplinary science synergetics has been closely connected with the emergence of laser theory. Synergetics deals with complex systems that possess the fundamental property of spontaneous selforganization of their macroscopic behaviour. The book summarizes basic ideas, important concepts and principles used to describe selforganizing systems from a unified viewpoint. Special attention is paid to lasers, nonlinear optics and to coherence phenomena in other physical, biological and sociological systems. Some surveys of historical developments are presented, but most space is devoted to the publication of recent results and the description of current research work.