Table Of ContentSynergetics
Springer-Verlag Berlin Heidelberg GmbH
C
ONLINE LIBRARY
Physics and Astronomy
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Hermann Haken
Synergetics
Introduction and Advanced Topics
With 266 Figures
, Springer
Professor Dr. Dr. h.c. multo Hermann Haken
Institute for Theoretical Physics I
Center of Synergetics
University of Stuttgart
PfaffenwaIdring 57/IV
70550 Stuttgart, Germany
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This book appeared originally in two volumes in the series "Springer Series in Synergetics":
Synergetics, 3rd Edition (1983)
Advanced Synergetics, 1st Edition (1983)
ISBN 978-3-642-07405-9 ISBN 978-3-662-10184-1 (eBook)
DOI 10.1007/978-3-662-10184-1
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Preface
This book is a reprint edition that comprises two titles, namely "Synergetics. An
Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics,
Chemistry and Biology" and ''Advanced Synergetics. Instability Hierarchies of Self
Organizing Systems and Devices". The reason for this publication is two-fold:
Since synergetics is a new type of interdisciplinary field, initiated by the author
in 1969, the basic ideas developed in these volumes are of considerable theoretical
interest. But much more than this, the methods and even the concrete examples
presented in these books are still highly useful for graduate students, professors, and
even for researchers in this fascinating field. The reason lies in the following facts:
Synergetics deals with complex systems, i.e. systems that are composed of many
individual parts that are able to spontaneously form spatial, temporal or functional
structures by means of self-organization. Such phenomena occur in many fields
ranging from physics, chemistry and biology to economy and sociology. More
recent areas of application have been found in medicine and psychology, where
the great potential of the basic principles of synergetics can be unearthed. Further
applications have become possible in informatics, for instance the designing of new
types of computers, and in other fields of engineering. The central question asked by
synergetics is: Are there general principles of self-organization irrespective of the
nature of the individual parts systems are composed of?
Indeed, the original books "Synergetics" and "Advanced Synergetics" provide
the reader with a solid knowledge of basic concepts, theoretical tools and mathemat
ical approaches to cope with the phenomenon of self-organization from a unifying
point of view. Synergetics takes into account deterministic processes as treated in
dynamic systems theory including bifurcation theory, catastrophy theory, as well
as basic notions of chaos theory and develops its own approaches. Equally well
it takes into account stochastic processes that are indispensable in many appli
cations especially when qualitative changes of systems are treated. An important
special case refers to non-equilibrium phase-transitions that were originally treated
in physics.
The longevity of these two books derives from the timelessness of mathematics.
But also the explicit examples of applications to various fields are still of a paradig
matic character. The wide applicability of the results of synergetics stems from the
fact that close to instability points were systems change their spatio-temporal pat
terns or functions dramatically, similar behavior may be demonstrated in a great
VI Preface
variety of systems belonging to many different fields. Thus "universality classes"
can be established. This has the advantage that once one has understood the behavior
of one system, one may extrapolate this behavior to other systems.
The "hard core" of the research strategy, as outlined in this volume, is as follows:
Nearly all systems are subject to influences from their environment. These influences
are quantified by control parameters. When these parameters change, the system may
adopt smoothly, or may change qualitatively. We focus our attention on the latter
situation, which is, of course, most interesting. Here, in large classes of systems that
are originally described by many variables, the behavior of a system is described
and determined by only few variables, the order parameters. They fix the behavior
of the individual parts via the slaving principle. The order parameter equations
that I derive are stochastic differential equations. I call them generalized Ginzburg
Landau equations because they contain the famous Ginzburg-Landau equations
as a special case. No prior knowledge of these equations is needed in this book,
however.
In order to motivate the reader to familiarize himself/herself with the detailed
mathematical approach that has led to these general insights and numerous explicit
applications, I will list some examples that are, of course, not exhaustive. Many
further examples as well as mathematical methods can be found in the volumes
of the Springer Series in Synergetics. I want to emphasize that a number of these
volumes add new important aspects to the just mentioned "hard core" and thus reflect
the central intention of the Springer Series in Synergetics, namely to provide the
science community with a forum for an in-depth discussion on the ways we can
deal with complex systems. Clearly over the past years quite a number of books and
numerous papers have been published outside the Springer Series in Synergetics,
but surely these have been in the spirit of the "Synergetics Enterprise". But now,
let me list some examples to which I give some typical references both outside and
inside the Springer Series. The latter references are indicated by "SSyn" and can
be found at the end of this book. The reader will understand that in view of the
vast field of applications of synergetics my list can contain only a small selection of
references.
Physics:
Spatio-temporal patterns (Staliunas, Sanchez-Morcillo, Gaul (2003», (Rosanov
(SSyn 2002» and stochastic properties of laser light, of fluids (Xu (SSyn 1997»
and plasmas, of currents in semiconductors (Scholl (2001» and of active lattices
(Nekorkin and Velarde (SSyn 2002».
Chemistry:
Formation of spatio-temporal patterns at macroscopic scales in chemical reactions.
for example the Belousov-Shabotinsky reaction (Babloyantz (1986). Nicolis (1995),
Mikhailov (SSyn 1994), Mikhailov and Loskutov (SSyn 1996», also the chemistry
of flames.
Preface VII
Computer science:
Synergetic computer for pattern recognition and decision making (Haken (SSyn
2004». This type of computer represents a genuine alternative to the by now tradi
tional neuro-computers, to e.g. the Hopfield net.
Traffic science:
This field has become a truly interdisciplinary enterprise. Here typical synergetic
phenomena can be discovered such as phase transitions in traffic flows (Helbing
(1997».
Biology:
Morphogenesis:
Based on Turing's ideas, synergetics calculates spatial density distributions of
molecules, in particular gradients, stripes, hexagons, etc. as a function of bound
ary and initial conditions. In initially undifferentiated omnipotent cells molecules
are produced as activators or inhibitors that diffuse between cells and react with
each other and thus can be transformed. At places of high concentration the activator
molecules switch on genes that, eventuaIly, lead to ceIl differentiation (Haken (this
book), Murray (2002».
Evolution:
By means of synergetics new kinds of analogies between biological and physical
systems have been unearthed. For instance, equations established by Eigen (Eigen
and Schuster (1979» for prebiotic, i.e. molecular evolution, turn out to be isomorphic
to specific rate equations for laser light (photons), where a specific kind of photon
wins the competition between different kinds of photons.
Population dynamics:
Resources, such as food, nesting places for birds, light intensity for plants, etc.
serve as control parameters. The numbers or densities of the individuals of species
serve as order parameters. Specific examples are provided by the Verhulst equation
or the preditor-prey relation of the Lotka-Volterra equations. Of particular interest
are dramatic changes, for instance the dying out of species under specific control
parameter values. This has influences on environmental policy. If specific control
parameters exceed critical values, the system's behavior can change dramatically.
For instance beyond a specific degree of pollution, the fish population of a lake wilI
die out.
Rhythms:
Nearly all biological systems show more or less regular periodic oscillations or fluc
tuations. These can be imposed on the system from the outside, for instance by the
day /night cycle (circadian rhythms), seasons, etc. (exogenous), or can be produced
by the system itself (endogenous). In the foreground of synergetics research are
VIII Preface
endogenous rhythms that may proceed on quite different spatial and temporal scales
(Haken and Koepchen (SSyn 1992), Mikhailov and Calenbuhr (SSyn 2002)). Exam
ples are cell metabolism, the circadian rhythms, brain waves in different frequency
bands (see below), cycles of menstruation, and rhythms in the cardiovascular system
(Stefanovska (2002)).
Movement science:
Rhythmical movements of humans and animals show well defined patterns of
coordination of the limbs, for instance walking, running of humans or gaits of
quadrupeds. Synergetics studies in particular transitions between movement pat
terns, for instance the paradigmatic experiment by Kelso (Kelso (1995)). If subjects
move their index fingers parallel at a low movement frequency, suddenly at an
increased frequency an abrupt involuntary transition to a new symmetric move
ment occurs. The control parameter is the prescribed finger movement frequency,
the order parameter is the relative phase between the index fingers (Haken (SSyn
1996)). The experimentally proven properties of a nonequilibrium phase transition
(critical fluctuations, critical slowing down, hysteresis) substantiate the concept of
self-organization and exclude that of a fixed motor program. Numerous further
coordination experiments between different limbs can be represented by the Haken
Kelso-Bunz model (Kelso (1995), Haken (SSyn 1996)). Gaits of quadrupeds and
transitions between them were modelled in detail (Schoner et al. (1990)), see also
(Haken (SSyn 1996)). These results have lead to a paradigm change in movement
science.
Visual perception:
The recognition of patterns, e.g. of faces, is interpreted as the action of an associative
memory in accordance with usual approaches. Here incomplete data (features) with
which the system is provided from the outside are complemented by means of data
stored in the memory. A particular aspect of the synergetic approach is the idea that
pattern recognition can be conceived as pattern formation. This is not only meant as
a metaphor, but means also that specific activity patterns in the brain are established.
In pattern formation a partly ordered pattern is provided to the system, whereby
several order parameters are evoked that compete with each other dynamically. The
control parameters are so-called attention parameters that in cases without bias are
assumed to be equal. The winning order parameter imposes the total pattern on
the system according to the slaving principle. This process is also the basis of the
synergetic computer developed by Haken (Haken (SSyn 1995)).
Gestalt psychology:
As is shown in Gestalt psychology, Gestalt is conceived as an entity to which in
synergetics an order parameter with its synergetic properties (slaving principle!) can
be attached. In principle, the recognition process of Gestalt proceeds according to
the synergetic process of pattern recognition. The winning order parameter gener
ates, according to the slaving principle, an ideal percept that is the corresponding
Preface IX
Gestalt. In ambiguous patterns an order parameter is attached to each percept of
an object. Because in ambiguous figures two or several possibilities of interpreta
tions are contained, several order parameters participate in the dynamics, whereby
the attention parameters become dynamical quantities. (For a comprehensive treat
ment of this and related topics see Kruse and Stadler (SSyn 1995).) As already
assumed by W. Kohler (Kohler (1920, 1955» and as is shown by the synergetic
equations, the corresponding attention parameter saturates, i.e. it becomes zero,
when the corresponding object has been recognized and the other interpretation
now becomes possible, where again the corresponding saturation process starts,
etc. Our model equations allow us also to take into account bias (Haken (SSyn
2004».
Psychology:
According to the concept of synergetics, psychological behavioral patterns are gen
erated by self-organization of neuronal activities under specific control parameter
conditions and are represented by order parameters. In important special cases, the
order parameter dynamics can be represented as the overdamped motion of a ball in
a mountainous landscape. By means of changes of control parameters, this landscape
is deformed and allows for new equilibrium positions (stable behavioral patterns).
This leads to new approaches to psychotherapy: destabilization of unwanted behav
ioral patterns by means of new external conditions, new cognitive influences, etc.
and measures that support the self-organization of desired behavioral patterns. This
comprises also the administration of appropriate drugs (e.g. neuroleptica), that in
the sense of Synergetics act as control parameters. The insights of synergetics have
been applied in the new field of Psychosynergetics with essential contributions by
Schiepek, Tschacher, Hansch, Ciompi and others (Schiepek (1999), Tschacher et al.
(SSyn), Hansch (2002), Ciompi (1982».
Brain theory:
Several books of the Springer Series in Synergetics are devoted to this field as well
as to experiments (KrUger (SSyn 1991), Ba§ar (SSyn 1998), Ba§ar et al. (SSyn
1983), Uhl (SSyn 1998), Tass (SSyn 1999), Haken (SSyn 1995, 2002». Also H.R.
Wilsons's fine book (1999) deserves attention in this context.
According to a proposal by Haken, the brain of humans and animals is conceived
as a synergetic, i.e. self-organizing system. This concept is supported by experiments
and models on movement coordination, visual perception, Gestalt psychology and
by EEG and MEG analysis (see below). The human brain with its 1011 neurons (and
glia cells) is a highly interconnected system with numerous feedback loops. In order
to treat it as a synergetic system, control parameters and order parameters must be
identified. While in synergetic systems of physics, chemistry and partly biology, the
control parameters are fixed from the outside, for instance by the experimentor, in
the brain and in other biological systems the control parameters can be fixed by the
system itself. In modelling them it is assumed, however, that they are practically
time-independent during the self-organization process. Such control parameters can
be, among others, the synaptic strengths between neurons that can be changed
