Chaos and Statistical Methods Proceedings of the Sixth Kyoto Sum

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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 well as stochastic processes. Volume 1 Synergetics An Introduction ByH. Haken Volume 2 Synergetics A Workshop

3rd Edition

Editor: H. Haken

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

Editors: A Pacault and C. Vidal

Editors: W Giittinger and H. Eikemeier

Volume 5 Pattern Formation by Dynamic Systems and Pattern Recognition Editor: H. Haken Editor: H. Haken

Volume 6 Dynamics of Synergetic Systems Volume 7 Problems of Biological Physics

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 Critical Phenomena Editors: 1. Della Dora, 1. 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 Chemical 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 Chemical Oscillations, Waves, and Turbulence Volume 20 Advanced Synergetics

By Y. Kuramoto

By H. Haken

Volume 21 Stochastic Phenomena and Chaotic Behaviour in Complex Systems Editor: P. Schuster Volume 22 Synergetics - From Microscopic to Macroscopic Order Editor: E. Frehland Volume 23 Synergetics of the Brain

Editors: E.

Volume 24 Chaos and Statistical Methods

Ba~ar,

H. Flohr, H. Haken, and AJ. Mandell

Editor: Y. Kuramoto

Chaos and Statistical Methods Proceedings of the Sixth Kyoto Summer Institute, Kyoto, Japan September 12 -15, 1983

Editor: Y. Kuramoto With 123 Figures

Springer-Verlag Berlin Heidelberg New York Tokyo 1984

Professor Dr. Yoshiki Kuramoto Research Institute for Fundamental Physics, Yukawa Hall, Kyoto University Kyoto 606, Japan

Series Editor: Professor Dr. Dr. h. c. Hermann Haken lnstitut fUr Theoretische Physik der Universitiit Stuttgart, Pfaffenwaldring 57/IV, D-7000 Stuttgart 80, Fed. Rep. of Germany

ISBN-13: 978-3-642-69561-2 e-ISBN-13: 978-3-642-69559-9 DOl: 10.1007/978-3-642-69559-9 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