Advanced Synergetics Instability Hierarchies of Self-Organizing

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 cept

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Editor: Hermann Haken

Synergetics, an interdisciplinary field of research, is concerned with the cooperation of individual parts of a system that produces macroscopic spatial, temporal or functional structures. It deals with deterministic as weH as stochastic processes. Volume 1 Synergetics An Introduction 3rd Edition ByH. Haken Volume 2 Synergetics A Workshop

Editor: H. Haken

Volume 3 Synergetics Far from Equilibrium Volume 4 Structural Stability in Physics

Editors: A. Pacault and C. Vidal

Editors: W. Güttinger and H. Eikemeier

Volume 5 Pattern Formation by Dynamic Systems and Pattern Recognition Editor: H. Haken Volume 6 Dynamies of Synergetic Systems Volume 7 Problems of BiologicaI Physics

Editor: H. Haken By L. A. Blumenfeld

Volume 8 Stochastic Nonlinear Systems in Physics, Chemistry, and Biology Editors: L. Arnold and R Lefever Volume 9 Numerical Methods in the Study of CriticaI Phenomena Editors: J. Della Dora, J. Demongeot, and B. Lacolle Volume 10 The Kinetic Theory of Electromagnetic Processes Volume 11 Chaos and Order in Nature

By Yu. L. Klimontovich

Editor: H. Haken

Volume 12 Nonlinear Phenomena in ChemicaI Dynamics

Editors: C. Vidal and A. Pacault

Volume 13 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences By C. W. Gardiner Volume 14 Concepts and Models of a Quantitative Sociology The Dynamics of Interacting Populations By W. Weidlich and G. Haag Volume 15 Noise-Induced Transitions Theory and Applications in Physics, Chemistry, and Biology By W. Horsthemke and R Lefever Volume 16 Physics of Bioenergetic Processes

By L. A. Blumenfeld

Volume 17 Evolution of Order and Chaos in Physics, Chemistry, and Biology Editor: H. Haken Volume 18 The Fokker-Planck-Equation

By H. Risken

Volume 19 ChemicaI Oscillations, Waves, and Turbulence Volume 20 Advanced Synergetics

By H. Haken

By Y Kuramoto

Hermann Haken

Advanced Synergetics Instability Hierarchies of Self-Organizing Systems and Devices

With 105 Figures

Springer.:verlag Berlin Heidelberg New York Tokyo 1983

Professor Dr. Dr. h.c. Herrnann Haken Institut für Theoretische Physik der Universität Stuttgart, Pfaffenwaldring 57 IN D-7000 Stuttgart 80, Fed. Rep. ofGermany

ISBN-13: 978-3-642-45555-1 001: 10.1007/978-3-642-45553-7

e-ISBN-13: 978-3-642-45553-7

Library of Congress Cataloging in Publication Data. Haken, H. Advanced synergetics. (Springer series in synergetics ; v. 20) 1. System theory. 2. Self-organizing systems. L Title. 11. Series. Q295.H34 1983 003 83-340 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means and storage in data banks. Under § 54 of the German Copyright Law where co pies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1983 Softcover reprint of the hardcover 1st ed ition 1983 The use of registered na