Table Of ContentSpringer Series in Synergetics
Editor: Herml,UlIl Haken
Synergetics, an interdisciplinary field of research, is concemed with the cooper
ation 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 2nd Edition
ByH. Haken
Volume 2 Synergetics A Workshop
Editor: H. Haken
Volume 3 Synergetics Far from Equilibrium
Editors: A. Pacault and C. Vidal
Volume 4 Stmctural Stability in Physics
Editors: W. Güttinger and H. Eikemeier
Volume 5 Pattern Formation by Dynamic Systems and Pattern Recognition
Editor: H. Haken
Volume 6 Dynamics of Synergetic Systems
Editor: H. Haken
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: J. Della Dora, 1. Demongeot, and B. Lacolle
Volume 10 The Kinetic Theory of Electromagnetic Processes
By Yu. L. Klimontovich
Volume 11 Chaos and Order in Nature
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
Evolution of
Order and Chaos
in Physics, Chemistry, and Biology
Proceedings of the International Symposium
on Synergetics at Schloß Elmau, Bavaria,
April 26 - May 1, 1982
Editor: H. Haken
With 189 Figures
SpringerVerlag Berlin Heidelberg New York 1982
Professor Dr. Hermann Haken
Institut fiir Theoretische Physik der Universität Stuttgart, Pfaffenwaldring 57/IV
D-7000 Stuttgart 80, Fed. Rep. ofGermany
ISBN-13: 978-3-642-68810-2 e-ISBN-13: 978-3-642-68808-9
DOl: 10.1007/978-3-642-68808-9
Library of Congress Cataloging in Publication Data. International Symposium on Synergetics (1982 : Schloss
Elmau, Bavaria). Evolution of order and chaos in physics, chemistry, and biology. (Springer series in
synergetics ; v. 17). Bibliography: p. Includes index. 1. System theory--Congresses. 2. Order-disorder models-
Congresses. 3. Physics--Congresses. 4. Chemistry--Congresses. 5. Biology--Congresses. I. Haken, H. 11. Title.
III. Title: Synergetics. IV. Series. Q295.1586 1982 50182-16891
ur
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© by Springer-Verlag Berlin Heidelberg 1982
Softcover reprint of the harcover 1s t edition 1982
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Preface
These proceedings contain the invited lectures presented at the International Sym
posium on Synergetics at Schloss Elmau in April, 1982. This symposium marked the
10th anniversary of symposia on synergetics, the first of which was held at Schloss
Elmau in 1972. As is now weIl known, these symposia are devoted to the study of the
formation of structures in physical systems far from thermal equilibrium, as weIl
as in nonphysical systems such as those in biology and sociology.
While the first proceedings were published by Teubner Publishing Company in 1973
and the second by North Holland Publishing Company in 1974, the subsequent proceed
ings have been published in the Springer Series in Synergetics. I believe that
these proceedings give a quite faithful picture of the developments in this new
interdisciplinary field over the past decade.
As H.J. Queisser recently noted, the prefix "non", which is used quite frequent
ly in modern scientific literature in words such as "nonequilibrium", "nonlinear",
etc., indicates a new development in scientific thinking. Indeed, this new develop
ment was anticipated and given a framework in the introduction of "synergetics"
more than a decade ago.
As everywhere in science, two main tendencies are visible here. On the one hand,
we note the achievement of more and more detailed results, and on the other hand,
the development of new unifying ideas. In synergetics the latter is unquestionably
the main goal. The Springer Series in Synergetics endeavors to attain this goal in
two ways. It provides a forum for interdisciplinary discussion by collecting the
relevant detailed experimental and theoretical results, and it presents new con
cepts under which the various phenomena can be subsumed.
The main objective of synergetics was initially the study of the far-reaching
analogies between quite different systems far from thermal equilibrium when they
pass from disordered states to ordered states. In such transitions, temporal or
spatial structures are created in a self-organized fashion on macroscopic scales.
Over the past years, a remarkable confluence of ideas has taken place, and a large
number of such transitions, which occur in close analogy with phase transitions of
thermal equilibrium, have come to be understood.
It soon became apparent that in such systems a hierarchy of various transitions
can take place when external conditions are changed. The question of universal
features has again arisen, and a whole new cl ass of phenomena, described as chaos,
has become a focus of scientific study. By chaos we mean seemingly random motion
which is described by deterministic equations. While at the beginning of these
studies the randomness of such phenomena was the principal interest, over the past
years it has become more and more evident that there are again considerable regu
larities to be observed experimentally and to be found mathematically. The dis
covery of such regularities has become an intriguing enterprise. In this respect
the present volume must be seen in close connection with the previous book pub
lished in this series, "Chaos and Order in Nature".
The present proceedings also mark another shift of emphasis within the field of
synergetics. While the emphasis has thus far been placed on dramatic changes in
systems on macroscopic scales, such changes may, of course, also occur on the
microscopic level, and I am very pleased to be able to include in these proceedings
a paper by M. Eigen on the evolution of biomolecules. In this fascinating field
of research, an intimate connection exists between dramatic changes on the micro
scopic, molecular level, and changes on the macroscopic, phenotypic level.
VI
This symposium on synergetics was made possible by a grant from the "Stiftung
Volkswagenwerk", Hannover, and I would like to take this opportunity to thank the
VW-Foundation for its continued and active support of the synergetics project.
I also wish to thank my secretary, Mrs. U. Funke, for her efficient help in
organizing this symposium and editing these proceedings.
Stuttgart, June 1982 H. Haken
Contents
Part I Introduction
Introductory Remarks. By H. Haken (With 1 Figure) 2
Part 11 Evolution
Ursprung und Evolution des Lebens auf molekularer Ebene
By M. Eigen (With 7 Figures) ...•....•...•..•..•...........•...••.•...... 6
Part /11 Coherence in B iology
The Crystallization and Selection of Dynamical Drder in the Evolution of
Metazoan Gene Regulation. By S.A. Kauffman (With 6 Figures) ..........•.. 26
The Synergetics of Actin-Myosin in Active Streaming and Muscle Contraction
By H. Shimizu (With 11 Figures) ..............•.......•..••.............• 36
Part I V Instabilities and Pattern Formation in Physics, Chemistry, and Biology
Pattern Formation in Magnetic Fluids. By R.E. Rosensweig (With 13 Figures) ..• 52
Thermoelastic Instabilities in Metals
By C.E. Bottani and G. Caglioti (With 8 Figures) 65
Spatial Chemical Structures, Chemical Waves. A Review
By C. Vidal and A. Pacault (With 6 Figures) ......•.•••...•••.......•.... 74
Spontaneous Biological Pattern Formation in the Three Dimensional Sphere.
Prepatterns in Mitosis and Cytokinesis. By A. Hunding (With 5 Figures). ..• 1DO
Generation of Projections in the Developing and Regenerating Nervous System
By A. Gierer ..........................•..•.......•.........•.•.........• 112
Part V Order and Chaos in Quantum Electronics and Fluids
Optical Bistability, Self-Pulsing and Higher Order Bifurcations
By L.A. Lugiato, V. Benza, and L.M. Narducci (With 13 Figures) 120
Benard Convection and Laser with Saturable Absorber. Oscillations and Chaos
By M.G. Velarde (Wifh 13 Figures) ........•.•....•.........••............ 132
Bistability and Chaos in NMR Systems
By D. Meier, R. Holzner, B. Derighetti, and E. Brun (With 12 Figures) 146
The Onset of Turbulence in the Wake of an Ion
By G. Careri (With 2 Figures) .•.•........•.•.•...•.......•.. ..•..•. ..... 157
Part VI Order in Chaos
Diversity and Universality. Spectral Structure of Discrete Time Evolution
By S. Grossmann (With 10 Figures) .•.•.............•••..•.....•.•..•....• 164
VIII
Onset of Chaos in Fluid Dynamics
By M. Giglio, S. Musazzi, and U. Perini (With 9 Figures) 174
Transition to Chaos for Maps with Positive Schwarzian Derivative
By G. Mayer-Kress and H. Haken (With 2 Figures) ..........•.............. 183
Scaling Properties of Discrete Dynamical Systems
By T. Geisel and J. Nierwetberg (With 9 Figures) •....................... 187
Phase Transitions in the Homoclinic Regime of Area Preserving Diffeomorphisms
By H.O. Peitgen (With 17 Figures) .......•..........••...••..••.•...•••.. 197
Noise Scaling of Symbolic Dynamics Entropies
By J.P. Crutchfield and N.H. Packard (With 8 Figures) 215
Dimension, Fractal Measures, and Chaotic Dynamics
By J.D. Farmer (With 10 Figures) .••..•..•.•..•••......•..•.•..•••.....•. 228
Part VII Chaos in Quantum Systems
Cooperative and Chaotic Effects in a Hamiltonian Model of the Free-Electron
Laser. By R. Bonifacio, F. Casagrande, and G. Casati (With 3 Figures) 248
Chaos in Quantum Mechanics. By G. Casati (With 2 Figures) 255
Part VIII Emergence of Order or Chaos in Complex Systems
Criticality and the Emergence of Structure. By P. Whittle (With 2 Figures) ..• 264
Strange Stability in Hierarchically Coupled Neuropsychobiological Systems
By A.J. Mandell, P.V. Russo, and S. Knapp (With 20 Figures) •........•... 270
List of Contributors 287
Part I
Introduction
Introductory Remarks
H. Haken
Institut für theoretische Physik der Universität
0-7000 Stuttgart 80, Fed. Rep. of Germany
Let us briefly recall what the aims of synergetics are. The word
"synergetics" is composed of Greek words meaning "working together".
Practically all systems can be thought of being composed of individual
parts such as atoms, molecules, cells, organs, animals,etc. In most
cases the individual parts form an entity which may produce
patt~rns,
structures, or functions on macroscopic scales. Quite often the total
system exhibits new qualities which are not present at the level of
the individual parts, and at least in same disciplines the cooperation
of the individual parts appears to be meaningful or purposeful.
In synergetics we ask the question whether there are general
principles which govern the selforganized behavior of such systems.
Both in the inanimate and animate world we find numerous kinds of
structures such as snowflakes, or patterns like rolls, hexagons, or
square patterns in fluids which are heated from below. In chemistry
we observe chemical waves, spirals, or chemical turbulence. The
formation of patterns like stripes or dots on furs or of rings on
butterfly wings has become accessible to modelling by means of
certain reaction diffusion equations.
A whole class of theories in biology can be now subsumed under this
"paradigm"which due to its originator might be called Turing's
paradigm. But while in the beginning, processes of cell differentiation
leading to macroscopic patterns were in the foreground of interest,
the present proceedings contain at least two new aspects. In this
contribution Hunding shows how an understanding of mytosis may
become possible by use of such concepts and Gierer presents his inter
esting ideas how topologically correct connections between sensory
organs and the corresponding neuronal net can be established.
At a still higher level it seems that we are about to understand
the formation öf organs, such as wings and feet of insects. Progress
has also been made over the past decade in the understanding of tem
poral patterns or functions. A standard example for selfsustained
oscillations, i.e .. a temporal structure, is provided by the laser
and by many further phenomena dealt wlth by quantum optics and
quantum electronics. Important new results are reported in the
subsequent contributions by Lugiato, Narducci, Velarde, Brun and
others. Selfsustained oscillations may be found in quite different
fields also, such as oscillations of rolls in the Taylor instability
in fluid dynamics, and oscillating chemical reactions of which the
Belousov-Zhabotinsky reaction is but one.
Biology provides us with a wealth of rhythms and even brain waves
indicate the cooperativity of neurons at a macroscopic level. At
this instant one should add a warning, however. Namely higher degree
of order does not necessarily imply a higher content of meaning.
For instance Figure 1 shows an EEG, where the upper part refers to
normal brain activity while the lower part refers to brain waves
in epileptic seizures. Using modern scientific language, we are
