Table Of ContentSpringer Series in Synergetics
Editor: Hermann Haken
Synergetics, an interdisciplinary field of research, is concerned 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 3rd Edition
By H. Haken
Volume 2 Synergetics A Workshop Editor: H. Haken
Volume 3 Synergetics Far from Equilibrium Editors: A. Pacault and C. Vidal
Volume 4 Structural Stability in Physics Editors: W. Giittinger 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: 1. 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-P1anck-Equation By H. Risken
Volume 19 Chemical Oscillations, Waves, and Turbulence By Y Kuramoto
Volume 20 Advanced Synergetics 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. Ba§ar, H. Flohr, H. Haken, and A. J. Mandell
Synergetics -
From Microscopic
to Macroscopic Order
Proceedings of the International Symposium
on Synergetics at Berlin, July 4 - 8, 1983
Editor: E. Frehland
With 146 Figures
Springer-Verlag
Berlin Heidelberg New York Tokyo 1984
Priv. Doz. Dr. Eckart Frehland
Fakultaten fUr Biologie und Physik, Universitat Konstanz, Postfach 5560,
D-7750 Konstanz, Fed. Rep. of Germany
Series Editor:
Professor Dr. Dr. h. c. Hermann Haken
Institut fUr Theoretische Physik der Universitat Stuttgart, Pfaffenwaldring 57IIV,
D-7000 Stuttgart 80, Fed. Rep. of Germany
ISBN -13 : 978-3-642-69542-1 e-ISBN -13 : 978-3-642-69540-7
DOl: 10.1007/978-3-642-69540-7
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2153/3130-543210
Preface
This volume contains the papers presented at the International Symposium on
"Synergetics - From Microscopic to Macroscopic Order", held at the Wissenschafts
kolleg z~ Berlin (Institute for Advanced Study Berlin), on July 4-8, 1983. Further
more, it contains a contribution of T. Ohta, who unfortunately could not partici
pate in this meeting, on the evolution of mUltigene families.
The papers discuss the evolution and the function of ordered structures from
small microscopic scales up to large macroscopic dimensions. On the one hand, these
structures derive from physical or biological systems; on the other hand, they also
affect economic, sociological and philosophical questions.
I would like to thank the Wissenschaftskolleg zu Berlin for the extraordinary
support and hospitality during my one year's stay there as a fellow, which made the
planning, preparation and organization of this symposium possible. I would also like
to acknowledge the work of B. Fritsch and D. Dorner who actively participated in
this undertaking.
I am grateful to Professor Haken, the founder of synergetics, whose participation
in the planning and styling of the concept of the conference was essential. I am
especially thankful to Mrs. U. Monigatti for her indefatigable help with the prep
aration and organization of the conference.
The financial support was provided by the "Deutsche Forschungsgemeinschaft".
Berlin, November 1983 E. Frehland
Contents
Some Introductory Remarks on Synergetics
By H. Haken ................................, ................................ .
Part I Order, Chaos, Indeterminancies
Time Pattern Transitions in Biochemical Processes
By B. Hess and M. Markus (With 6 Figures) .........................•......... 6
Chaotic Behaviours Observed in Homogeneous Chemical Systems
By C. Vidal (With 8 Figures) ................................................ 17
Wave-Number Selection in Rotating Couette-Taylor Flow
By G. Ahlers and D.S. Cannell (With 3 Figures) ............................... 27
Periodic and Chaotic Patterns in Selected Quantum Optical Systems
By L.M. Narducci, D.K. Bandy, J.Y. Gao, and L.A. Lugiato (With 16 Figures) 33
Chaos in Lasers
By R. Graham (With 4 Figures) 47
The Falling Pencil and Superfluorescence: Macroscopic Indeterminacies After
the Decay of Unstable Equilibria
By F. Haake (Wi th 5 Fi gures) ................................................. 58
Part II Ordered Structures and Processes in Biomembranes
On the Formation of Transient Order in Biological Membranes
By E. Sackmann (With 13 Figures) ............................................ 68
Generalized Moment Description of Brownian Dynamics in Biological Systems
By K. Schulten, A. BrUnger, W. Nadler, and Z. Schulten (With 4 Figures) 80
Nonequilibrium Current Noise Generated by Ordered Ion Transport Processes in
Biological Membranes By E. Frehland (With 8 Figures) ................. ...... 90
The Molecular Machine of Photosynthesis-Physico-Chemical Aspects
By H.T. Witt (With 3 Figures) ................... ............................ 99
Part III Evolution of Structures
Polynucleotide Replication and Biological Evolution
By P. Schuster (With 7 Fi gures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
The Evolution Strategy. A Mathematical Model of Darwinian Evolution
By I. Rechenberg (With 14 Figures) .......................................... 122
VII
Multigene Families and their Implications for Evolutionary Theory
By T. Ohta (With 5 Figures) ................................................. 133
Evolution of Biothermodynamic Systems
By J.U. Keller (With 3 Figures) .............................................. 140
Self-Organising Oynamic Models of Human Systems
By P.M. Allen, G. Engelen and M. Sanglier (With 18 Figures) 150
Part I V Social Sciences
Some Applications of Basic Ideas and Models of Synergetics to Sociology
By A. Wunderlin and H. Haken ................................................ 174
A Synergetic Approach to Energy-Oriented Models of Socio-Economic-
Technological Problems
By A.B. Cambel (With 6 Figures) ............................................. 183
New Synergisms in Socio-Economic Systems: More Questions than Answers
By B. Fri tsch .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 197
On the Entropy of Economic Systems
By D.T. Spreng (With 3 Figures) ...................................•......... 207
Part V Complex Systems
Death - From Microscopic to Macroscopic Disorder
By F. Cramer (With 11 Figures) ' .............................................. 220
Local Synaptic Modification Can Lead to Organized Connectivity
Patterns in Associative Memory
By G. Palm (With 5 Figures) ................................................. 229
The Organization of Action in Time
By D. Dorner (With 4 Figures) ............................................... 243
New Problems for an Old Brain - Synergetics, Cognition and Evolutionary
Epistemology
By G. Vollmer ............................................................... 250
Index of Contributors ••••••••••••.•.•••••••••••..•••••••••••••••••...••...••. 259
VIII
Some Introductory Remarks on Synergetics
Hermann Haken
Institut fUr Theoretische Physik, Universitat Stuttgart, Pfaffenwaldring 57/IV
0-7000 Stuttgart 80, Fed. Rep. of Germany
I am glad to make a few introductory remarks at this meeting on
"Synergetics, from microscopic to macroscopic order". The reader of
these proceedings may be puzzled by the variety of topics treated.
Therefore especially for those who are not familiar with the general
goal of synergetics a few words of explanation might be in order.
According to its definition, synergetics deals with systems composed
of many parts which can form spatial, temporal or functional structures
on macroscopic scales. Indeed most of the contributions to these pro
ceedings deal with such systems. Over the past decade numerous systems
in physics, chemistry and specific model systems of biology have been
studied in which macroscopic structures are formed through self
organization. Examples are provided by chemical oscillations, where
the molecules react in such a way that macroscopically a periodic
change of color or of other properties can be observed (cf. the
contribution by B. Hess). Such processes play an important role in
biology also. Another example is provided by different kinds of wave
formations in fluid dynamics and in lasers. In all these cases a
rather coherent picture could be drawn within the past decade. When
an external control parameter such as energy input or temperature
is changed, systems may run through a hierarchy of instabilities.
At each instability point a new macroscopic pattern replaces the
old one. It is by now well known that the transition from one macro
scopic pattern to another one obeys general principles which can be
formulated by order parameters and the slaving principle. I shall
not dwell here on the details of this approach because it has been
presented in two books of mine [1,21, and in quite a number of
contributions to proceedings of conferences and summer schools. I
rather wish to address myself to the problem in how far those general
concepts can be applied to other disciplines, especially those of
sociology and psychology.
Modern science is becoming more and more confronted with the
question of how to cope with complex systems. Examples are provided
by biological systems including the brain, or economy. A complete
description of the behavior of such systems seems to require an
enormous amount of information which nobody is able to handle.
Therefore it seems to be a problem of utmost important to find
means to compress information. In the realm of former work of syn
ergetics it could be shown that a compression of information becomes
possible close to instability pOints where the whole dynamics of the
complex system is governed by few order parameters only.
With respect to economy such a point of view may look revolu
tionary because, as it seems to me, a good deal of approaches in this
field are dealing with stable situations and are devoted to the
question of how to maintain stability. From the general point of
synergetics it seems to be, however, more interesting and even more
promising to study the behavior of complex systems at points of
instability. Instability in this technical context does not mean
that an economy breaks down but that it changes its behavioral
patterns. An example of this kind is provided by studies of Mensch
[3] on the transitions between full employment and underemploy
ment. Another example is provided by evolutionary models of socio
economic systems as in the paper presented by Allen at this sym
posium. According to our understanding,evolution may be visualized
as a sequence of instabilities at which over and over again new
patterns or structures
~merge.
In these evolutionary steps an important interplay between deter
ministic processes and fluctuations, i.e., random events, takes place.
In biology these fluctuations are, of course, represented by mutations.
The interplay between these two kinds of processes plays a fundamen
tal role, for instance in Rechenberg's approach to an optimization
of technical devices.
There are other fields of study in which an application of the
general ideas of synergetics may be less obvious. One of them is
photosynthesis where it may seem to be extremely difficult if not per
haps impossible to single out specific order parameters or use the
equivalent idea of macroscopic degrees of freedom. However, also in
this field the situation may change soon. For instance it has been
convincingly suggested by Blumenfeld in his monographs in the
Springer Series in Synergetics [4] that enzymes act as molecular ma
chines with few degrees of freedom. Indeed also in photosynthesis the
main problem seems to be to explain how the molecular machinery pre
vents a quick dissipation of energy into many degrees of freedom, i.e.,
into heat, and rather manages instead to keep the energy concentrated.
The contribution by G. Vollmer in "Synergetics, Cognition, and
Evolutionary Epistemology" seems to me particularly remarkable be
cause it elucidates the fact that synergetics is a scientific disci
pline whose principles can be applied to itself. Namely the evolution
of new scientific paradigms is nothing else but the emergence of a
new pattern of thoughts. This evolution obeys again the general rules
of synergetics, namely that of accidental fluctuations, competition
between collective modes, and survival of the fittest mode.
I should like to make a comment on the formation of associative
memory, a concept due to Kohonen [5] on which Palm reports in his
contribution to these proceedings. An important concept in that
approach rests on the idea of Hebb's synapse, often invoked in
theories of learning processes. According to this concept certain
synapses are strengthened if they are used more than others. At
first sight it seems as if such a concept is totally local and that
there is no relation with the global aspects of synergetics. However,
it may be worthwhile pointing out that quite close connections
between these two aspects can be established. For instance.it has
been shown by Haussler and von der Malsburg [6] that in retino-
topic processes, which in a way are related at the microscopic level
to the idea of Hebb's synapse, the concept of order parameters allows
one to deduce the macroscopically evolving pattern of connections
between retina and tectum. Invoking results from synergetics may
possibly resolve another puzzle. So far experimentally Hebb's idea
could notbe confirmed. In my interpretation this may be due to the
fact that in large enough nets of neurons even a tiny change of
synaptic connections may produce macroscopic effects. This implies
that an individual synapse may change very little which may escape
experimental study. I base my interpretation on the analogy with
laser physics where somewhat above laser threshold a small fraction
of the total activity of each individual atom suffices to produce
a coherent light wave. Thus I believe that the methods of synergetics
and the more microscopic approaches used in associative memory can
complement each other.
2
In conclusion I should like to make a rather general statement
on the role played by synergetics. Synergetics can be considered as
a forum where scientists from quite different disciplines meet each
other to exchange their ideas on how to cope with complex systems.
Looking back over the last decade I think it is fair to. say that
enormous progress has been achieved towards the understanding of
complex systems by searching for unifying principles. I am convinced
that not only for philosophical but also for quite practical and
pragmatic reasons it will be necessary to search further for uni
fying mathematical structures without whose help we can hardly deal
adequately with complex systems.
References
H.Haken: Synergetics. An Introduction, 3rd ed.
(Springer, Berlin, Heidelberg, New York 1983)
2 H.Haken: Advanced Synergetics. Instability Hierarchies of Self
Organizing Systems and Devices, Springer, Berlin, Heidelberg,
New York 1983
3 G.Mensch, K.Kaasch, A.Kleinknecht, R.Schnopp: Discussion
paper series, Internat.lnstitute of Management, Wissenschafts
zentrum Berlin (1950-1978)
4 L.A.Blumenfeld! Problems of Biological Physics, Springer,
Berlin, Heidelberg, New York 1981
L.A.Blumenfeld: Physics of Bioenergetic Processes, Springer,
Berlin, Heidelberg, New York 1983
5 T. Kohonen: Associative Memory, Springer, Berlin, Heidelberg,
New York 1977
6 A.F.Haussler and C.von der Malsburg, J.Theor.Neurobiol.
in press
3
