CCSR Technical Reports,
with Abstracts: 1990-94
Technical Reports, with Abstracts: 1994
The Second Metamorphosis of Science: A Working Paper
, Technical Report CCSR-94-1
Abtract: During the period of approximately 1570-1790 the first metamorphosis
of science transformed the operational foundations of science, that were largely the heritage
from the time of Aristotle, into its modern form. These new foundations consisted of the
use of (1) Physical Experiments and the use of (2) Mathematical Models, involving differential
equations. This metamorphosis was largely due to Brahe, Kepler, Galileo, Newton, Leibnitz,
Euler, and Lagrange. These operational methods were accompanied by the development of
several philosophical attitudes and beliefs. One attitude (an implicit but operative frame of
mind) arose from the loss of concern about the limitations of the encoding and decoding of
information between experiments and mathematics; that is, an increased identification of
the physical world with the mathematical models used to make very limited predictions of
that world. The more overt philosophical beliefs related to the fundamental character of reductionistic
methods in science. Among these beliefs was the idea that it is possible to synthesize this reductionistic
knowledge, thereby obtaining a theory of the universe, capable of predicting all phenomena in nature.
The idea that there is indeed any such thing as one set of laws which govern the behavior of the
universe has its origins in antiquity, where the laws often referred to the desires of a god. This
belief was immeasurably reinforced within Science by the success of Newton's 'universal law' of
gravitation. The blending of these persuasions was perhaps captured best, intended or not, in
Einstein's famous remark, "I shall never believe that God plays dice with the world."
past century the character and structure of science has been going through a second process of
fundamental change which has been brought about by two classes of discoveries. The first
group of discoveries concern mathematical results which are directly related to the limitations
in what we can learn about the dynamic behaviors in nature from these mathematical models.
The discoveries of these limitations should have produced a 'loss-of-innocence' era, but they
have largely gone unnoticed by scientists, even though they have profound implications concerning
the future character of science. Among these discoveries, which apply to essentially all mathematical
models of physical systems, are our inherent limitations to make: (1) analytic mathematical
deductions, (2) deterministic physical predictions, and (3) structurally stable models of closed
systems. In addition, other mathematical discoveries were made which struck at the basic idea
that mathematical systems are consistent, and can establish any result which is true. Each of
these discoveries have, or will have, a direct impact on the philosophical preconceptions of many
scientists, since they shatter widely held beliefs about our ability to extract (deduce) information
about nature only through the use of mathematical modeling and analysis, together with physical
experiments. Physical experiments also stimulated other mathematical studies that further confirmed
this lack of physical predictability. These results establish that our knowledge about the behavior of
complex systems is limited to 'comprehensible' sets of observables (windows of comprehension),
that involved 'bounded reducibility', and also establish that we are only capable of bounded predictability
of physical events (proportional to our bounded information about the state of the system).
second half of this century a totally different class of opportunities and discoveries have been made
possible by a new operational basis for scientific investigations, due to the digital computer. This
expanded the operational bases of (1) Physical Experiments, and (2) Mathematical Models, established
during the first metamorphosis, to include the third operational basis for obtaining knowledge about
nature, that will be referred to as (3) Computer Experiments. Operations carried out in each of these
three areas can yield independent knowledge relevant to our understanding of nature, and can interface
directly with either of the other two areas. In particular, the lost deductive dreams concerning mathematical
models, the information encoding-decoding limitations that exist between physical experiments and
mathematical solutions, and the bifurcation processes of dynamical models, have already been clarified
and extended by Computer Experiments. Some of the numerous potentials for this interplay between the
three operational methods is discussed below. For example, information about the dynamics of physical
systems can be achieved using the interface between Computer Experiments and Physical Experiments,
which does not rely on any mathematical modeling (or algorithms) related to the observables of the
physical system. Moreover, using only this experimental information, limited predictions can be
made without any dynamic models. Also certain types of local and global mathematical models
can be sought, which is a simple form of computer/human induction. Computer Experiments
also allow for the search of dynamics (algorithms) which scientists have not been capable of
imagining in their inductive dreams; a more profound form of the computer inductive process
is related to ongoing developments of computer 'genetic' dynamics. Computer Experiments
can graphically represent incomprehensible data sets, and can search for 'emergent' properties
of complex systems. Also there is is a branch of research that is exploring fundamental issues
related to the possible finite-informational character of all dynamic phenomena, and its
natural association with both reconstruction methods and Computer Experiments.
the recognition of deductive limitations and the expanded operational foundation, the general
character of science is going through a process of metamorphosis which is both exciting in its
richness, and impossible to presently define with any precision. Some aspects of this metamorphosis,
and their bearing on widely held philosophical dreams of scientists, will be discussed.
Localized Measures for Non-Stationary Time-Series of Physiological Data
, Technical Report CCSR-94-2
Abtract: We will discuss localized measures related to the concepts of dimension,
Lyapunove exponents (entropy), and recurrence diagrams. We stress the relevance of
localized events and coincidences in physiological time series that often are lost when
statistical averaging methods are applied. We suggest event based statistics as an alternative
to spectral or averaged based statistics. The use of wavelets bases for characterizing localized
structures is discussed as a potential alternative to Fourier based analysis. Finally we mention
how local domains in state space could be applied as triggers for external stimuli and thereby
improve the statistics of ERP recordings.
Collective Phenomena in Spatially Extended Evolutionary Games
, Technical Report CCSR-94-3
Abtract: A class of spatially extended evolutionary games with simple local
rules is introduced. The emergent properties are studied through two complementary
approaches. One is based on a heuristic local analysis, the other on exact global techniques.
The local analysis provides criteria to form groups of games with distinct behavior.
The results facilitate numerical simulations and reveal that even simple games allow for
complex spatio-temporal phenomena. The global analysis demonstrates that certain games
perform an up-hill march in a fitness landscape determined by the payoff parameters and the
topology of the underlying lattice structure. For generic game parameters, the landscape is
rugged due to competing interactions and generates dynamical phenomena well known from
frustrated systems: trapping in local maxima for noiseless dynamics and very long relaxation
times for stochastic dynamics.
Although the model is a mere caricature of evolutionary
processes, some of its emergent properties are reminiscent of those observed in nature. It is
argued that similar dynamical phenomena will be present in more elaborate approaches.
The Changing Foundations of Science
, Technical Report CCSR-94-4
Abtract: In this article I will give brief outline of the changes that have
begun to occur in those sciences that attempt to understand natural phenomena. The
approach will be a 'bottom-up' organization of this field of activity, starting with the
most basic operations of generating scientific information, proceeding to the less objective
activities that relate these different forms of information ('scientific methods'), and finally
trying to uncover the new unifying programs of science. The ordering helps to eliminate
many ill-defined 'scientific' concepts, which greatly assists in focusing on the new basic
aspects and challenges in this wonderful changing scene.
This bottom-up ordering of
scientific activities will be organized into three tiers:
I) The three information-generating
operations used in modern science, and the distinct characteristics of their information.
The problems associated with the encoding/decoding of information between these operations,
and the multiple types of cyclic routes that can be used to connect these forms of information.
Each cycle yields a different type of 'scientific method', which is intended to validate our
understanding of some phenomenon.
III) Some of the questions that are related to the
new organizing principles of science, which are needed to replace the historic and discredited
program of microreduction-followed-by-deductive-syntheses (or simply, the reduction/synthesis
While each of these tiers involve a myriad of issues, I will attempt to select a few of
the most basic elements, following the above order.
G. Mayer-Kress, C. Barczys,
The Global Brain as a Modeling Paradigm for Crisis Management
, Technical Report CCSR-94-5
Abtract: We discuss how the existence of a global and tightly connected
network of computer workstations such as the Internet can lead to the emergence of a
globally self-organized structure that we would like to refer to as the
Global Brain. Associated with that structure would be the capability for a class
of highly distributed and interactive global models that can have a functional resemblance
to how biological brains solve complex problems. Though this article emphasizes worldwide
models for crisis management, the concept of a Global Brain and models which utilize
the Global Brain can be applied in any research area where models that are more rapid
and appropriate in their responses to ever-changing, non-equilibrium situations are desired.
We first discuss some functional properties of biological brains and how their functional
analog could be manifested in a Global Brain. We then present an eight-step process for
constructing models which utilize the Global Brain. We review some of the tools that are
currently available to make the information and simulation resources of the global Internet
system accessible to researchers wishing to participate in the development of this type of
model. We discuss some potential applications to regional crisis management that might result
from this approach. We conclude with a consideration of some of the implications of a Global Brain.
G. Mayer-Kress, W. Bender, J. Bazik,
Hyper-Media on the Internet as a Tool for Approaching Global Problems: A Tele-Conferencing Experiment
, Technical Report CCSR-94-6
Abtract: In this report we describe an experimental virtual participation in
a panel discussion of the Seventh Annual Hunger Research and Exchange via Internet and
telephone. The aim was to demonstrate an efficient and cost-effective way of virtual
conference participation, especially for researchers from third world countries. We used state
of the art hyper-media documents (using WWW/Mosaic) that were transferred to workstations
at the conference site, prior to the presentation. During the oral presentation via telephone, visual
aids were presented by a local operator who provided realtime feedback to the presenter via the Unix
E.A. Jackson, I. Grosu,
An Open-Plus-Closed-Loop (OPCL) Control of Complex Dynamic Systems
, Technical Report CCSR-94-7
Abtract: A new method of controlling arbitrary nonlinear dynamic systems,
dx⁄dt = F(x,t)(x∈Rn), is presented. It is proved that there exist
solutions, x(t), in the neighborhood of any arbitrary 'goal' dynamics g(t) that are entrained
to g(t), through the use of an additive controlling action, K(g,x,t) = H(dg⁄dt,g) + C(g,t)(g(t)-x)
, which is the sum of the open-loop (Hübler) action, H(dg⁄dt,g), and a suitable
linear closed-loop (feedback) action C(g,t). Examples of some newly obtained entrainment controls are given.
P. Jung, G. Mayer-Kress,
Stochastic Resonance in Threshold Devices
, Technical Report CCSR-94-8
Abtract: We consider the transmission of a periodic by noisy threshold devices.
A general expression for the input-output characteristic is developed and applied to two
particular threshold devices. It is shown that the amplitude of the signal output shows
in the sub-threshold regime a maximum as a function of the noise strength - the fingerprint
of stochastic resonance.
Threshold Devices: Fractal Noise and Neural Talk
, Technical Report CCSR-94-9
Abtract: We consider the statistical properties of random pulse trains generated
by noisy signals imposed on a threshold device - a simple model for the information processing
of a single neuron. It is shown that Markovian noise generates self-similar bursts characterized
by algebraic decaying correlations and power spectra. It is further shown that the role of noise
is ambiguous. For sub-threshold signals, noise can enhance the performance of a threshold device,
whereas above threshold noise always degrades a signal.
U. Parlitz, G. Mayer-Kress,
Predicting Low Dimensional Spatio-Temporal Dynamics Using Discrete Wavelet Transforms
, Technical Report CCSR-94-10
Abtract: A new method is presented for predicting spatio-temporal time series
whose dynamics is generated by a low-dimensional deterministic dynamical systems. It is
based on a combination of time delay embedding and wavelet expansion and is also applicable
in cases where the dynamics may not be linearly decomposed into the evolution of a small
number of spatial modes. As an example we predict chaotic transversal motions of two Gaussian
pulses along a one dimensional axes.
Transferring Dynamics Between Five Attractors of the Chua System
, Technical Report CCSR-94-11
Abtract: The Chua electronic circuit possess five attractors; one limit cycle,
two fixed points, a one-band and a three-band strange attractor. It is shown that, by
applying the open-plus-closed-loop control recently developed by Jackson and Grosu, it is
possible to reliably transfer the dynamics between any of the five attractors, without any
knowledge of the state of the system on the initial attractor. Of particular interest is that
this can be accomplished by the use of only five fixed-point goals, one for each of the final
attractors. Thus, in the basin of attraction of each attractor there exists a set of points whose
basins of entrainment contains all of the other attractors. Such a simple 'migration action'
can not be expected to hold for all systems.
R. Shermer, S. Balachandar, A. Hübler,
Forced Drag Modification on a Cylinder in a 2D Numerical Simulation
, Technical Report CCSR-94-12
Abtract: The theoretical development of an open loop control method loosely known as
control has suggested a systematic technique for controlling hydrodynamic systems without
feedback. Computing a driving force that yields a new mathematical solution to the system is
the fundamental idea behind the technique. The theoretical development is explored and the
stability of this method is verified in a computational setting using a verified pseudo-spectral
simulation of a two dimensional, incompressible Navier-Stokes flow past a cylinder. The first
simulation uses the ideal force (which is not physically realizable) to take an open channel flow
system with a radius Reynolds number of 60 to a stationary flow field state having a Reynolds
number of 5. The second simulation demonstrates the effect of restricting the driving force
to a thin boundary layer about the cylinder in order to achieve a physically applicable control.
The temporal entrainment process is shown and drag coefficients are measured. The ideal
driving force, its boundary layer approximation and physical implementation are also discussed.
D. Pierre, A. Hübler,
A Theory for Adaptation and Competition Applied to Logistic Map Dynamics
, Technical Report CCSR-94-13
Abtract: We present a theory for adaptive, predictive, and competitive agents
in an evolving chaotic environment. The agents are simple algorithmic agents designes
to model, predict, and exert open loop control on their environment. The environment
is the time iteration of the logistic map with external noise added. We find that passive
agents can make accurate single step predictions even if the environmental dynamics is
chaotic, while accurate multiple step predictions are possible only if the Liapunov exponent
of the environmental dynamics is negative. Multiple step predictions with high precision can
be made over a broad range of conditions when one agent exerts control on the environment.
When two agents are simultaneously attempting control of the environment an agent will
achieve the smallest prediction error when the second agent's goal dynamics has a stable
fixed point which coincides with a stable or unstable fixed point of the goal dynamics of
the first agent. When the fixed points of the goal dynamics of the two agents do not match,
we find that the prediction errors of both agents approaches a constant value while the
amplitudes of the driving forces grow at a constant rate. Further, our studies suggest that
generally the agent with the more complicated goal dynamics may achieve an extremely
small prediction error by a perfect entrainment of the environmental dynamics.
H. Nosaka, K. Tsuji, A. Hübler,
Optimal Control of Singular Motion
, Technical Report CCSR-94-14
Abtract: We study the control of overdamped motion of particle subject to
a non-smooth force. We find size of optimal control force is very small at the boundary
between singular and regular motion. In addition we find that linear feedback does not
stabilize control of singular motion. We show that the special type of feedback makes it
possible to stabilize the control of singular motion. We discuss impact of noise.
C. Wargitsch, A. Hübler,
System Identification With Stochastic Resonance
, Technical Report CCSR-94-15
Abtract: We study the impact of noise to the entrainment of underdamped
nonlinear oscillators to resonant driving forces. We find that the power consumption is
large at a certain noise level. In addition we find that the power consumption drops significantly
if the forcing function is off-resonant. We discuss possible applications for system identifications.
R. Mettin, W. Lauterborn, A. Hübler, A. Scheeline,
Parametric Entrainment Control
, Technical Report CCSR-94-16
Abtract: We present a generalized approach for model-based non-feedback
control of nonlinear dynamical systems that includes parametric dependence on the control
forces. For iterated maps and ordinary differential equations, we obtain entrainment to
stationary, periodic, and aperiodic goal dynamics. Applicability to general resonance
spectroscopy is demonstrated, and use in a case of restricted control is shown.
F. Yamaguchi, K. Kawamura, A. Hübler,
Sudden Drop of Dissipation in Field-Coupled Quantum Dot Transistor
, Technical Report CCSR-94-17
Abtract: We propose a novel device where energy loss accompanied by a current
flow through a resistor is recovered, and therefore Joule's heat production is exclusively low.
This "energy-recovery effect" is caused by dynamical transition due to electronic coherent i
nterference, namely Coulomb interaction within specially designed coupled-quantum dots.
We study characteristics of this device as a resistor. We find sudden drop of energy dissipation
due to the current flow as a function of the electro-chemical potential of the reservoir which
is coupled to the quantum dots. In addition, we show resistance of the device depends on
the strength of the Coulomb interaction.
S. Fujiwara, A. Hübler,
Chaotic Mixing by Kneading
, Technical Report CCSR-94-18
Abtract: We study the mixing process of kneading dough experimentally and
model it with a simple area-preserving map ("mixing map"). This map is characterized
by a parameter rsm
(1/2 ≤ rsm ≤ 1)
, which represents the ratio of "stretching" to "moving", and a map with rsm = 1
corresponds to a baker's transformation. We analyze mixing properties of this map by
applying the diagnostics of mixing used by I. Zawadzki and H. Aref (Phys. Fluids A 3, 1405 (1991)).
We find that mixing is very efficient at rsm = 1 but degrades rapidly nearby.
However at rsm ≈ 3/4 mixing is as efficient as a baker's transformation.
Accidentally, this parameter region rsm ≈ 3/4 is achievable experimentally.
PACS number(s): 05.45+b, 83.50.Ws
P. Jung, G. Mayer-Kress,
Noise Controlled Spiral Growth in Excitable Media
, Technical Report CCSR-94-19
Abtract: We consider a two-dimensional pulse-coupled array of noisy threshold
elements with a long-range interaction. For tight coupling, we observe the formation of
spatio-temporal excitation waves, such as target and spiral waves. For weak coupling,
we find noise sustained spiral growth, where the noise level controls the scale of the spiral.
P. Jung, P. Talkner,
Suppression of Higher Harmonics at Noise Induced Resonances
, Technical Report CCSR-94-20
Abtract: We consider the generation of higher harmonics in periodically
driven noisy nonlinear systems. Recent numerical studies of higher harmonics in such
systems have shown so-called noise induced resonances that manifest themselves
in a strong suppression of higher harmonics at certain values of the noise level. A theory
for this peculiar phenomenon is presented, unmasking the universal character of these
resonances and their widespread.
L. Arsenault, A. Hübler,
Dynamics of Damped Coupled Oscillators Near Resonance
, Technical Report CCSR-94-21
Abtract: We study the dynamics of two conservative oscillators with pertubations
from a linear displacement coupling and non-Hamiltonian forces such as damping. We
examine the dynamics of these systems when they are near the primary resonance using
secular pertubation theory. We show that near resonance a large class of driven oscillators
and two coupled oscillators can be transformed to the same ordinary differential equations (ODE's).
This common type of dynamics near the resonance is a generalization of the standard Hamiltonian
dynamics of two coupled conservative oscillators. We derive expressions for the parameters in
these ODE's. From these parameters, we derive analytical expressions for the linear fixed
point behavior of these oscillators near resonance. We find a relation between the amplitude
frequency coupling of the oscillators and their phase-locking behavior. In particular, we show
that two hard oscillators lock in phase and two soft oscillators lock out of phase. We compare
our theoretical predictions with computer simulations of two examples: a s sinusoidally
driven X3 force oscillator and two coupled van der Pol oscillators with X3 force.
G. Mayer-Kress, C. Barczys,
The Global Brain as an Emergent Structure from the Worldwide Computing Network, and its Implications for Modelling
, Technical Report CCSR-94-22
Abtract: We propose that the existence of a globally and tightly connected
network of computer workstations such as the Internet can lead to the emergence of a
globally self-organized structure which we refer to as the Global Brain.
with that structure would be the capability for higher levels of information processing
which can be harnessed to build new kinds of models that are more rapid and appropriate
in their responses to ever-changing, non-equilibrium situations. To gain insight into possible
characteristics of a Global Brain, we examine some functional properties of biological brains
and discuss how their functional analog could be manifested in a Global Brain.
explore the implications of a Global Brain for simulation modelling, and present an eight-step
process for constructing models which utilize the Global Brain. We review some of the tools that
are currently available to make the information and simulation resources of the global Internet
system accessible to researchers wishing to participate in the development of this type of model.
We discuss some potential applications to regional crisis management that might result from this
approach. We conclude with a consideration of some of the implications of a Global Brain.
R. Bartussek, P. Hänggi, P. Jung,
Stochastic Resonance in Optical Bistable Systems
, Technical Report CCSR-94-23
Abtract: We study the response of a noise-driven absorptive optical bistable system
which is subjected to deterministic periodic pertubations of the incident light intensity. This system is
characterized by state-dependent noise which in turn can strongly enhance - vis stochastic resonance -
the response due to the external periodic pertubation. We demonstrate that the condition for stochastic
resonance sensitively depends on the shape of the bistable generalized potential (symmetric or
asymmetric). Furthermore, the generation of higher harmonics is studied in the presence of
fluctuations. We report on a novel phase-sensitive resonance phenomenon which virtually
eliminates the higher harmonics and thus allows for distortion-free amplification of signals
via stochastic resonance.
C. Wargitsch, A. Hübler,
Resonances of Nonlinear Oscillators
, Technical Report CCSR-94-24
Abtract: We study the dynamics of nonlinear oscillators with aperiodic driving
forces. We find that these oscillators have a large response to special aperiodic driving forces.
These optimal forcing functions are given by the time-reflected transient of the unpertubed
dynamics when the size of the forcing function is measured with the L2-norm
(principle of the dynamical key). We provide a proof of this principle. We find that optimal
forcing functions have very similar dynamics for several different norms. We present a
quantitative comparison of the energy transfer for sinusoidal and optimal driving force. We
find that aperiodic driving forces are most effective for large nonlinearity and small friction.
For several important systems, we show that optimal control is stable
G. Mayer-Kress, W. Bender, J. Bazik,
A Tele-Conferencing Experiment with WWW/Mosaic
, Technical Report CCSR-94-25
Abtract: In this report we describe an experimental virtual participation in
a panel discussion of the Seventh Annual Hunger Research and Exchange via Internet and
telephone. The aim was to demonstrate an efficient and cost-effective way of virtual conference
participation, especially for researchers from third world countries. We used state of the art
hyper-media documents (using WWW/Mosaic) that were transferred to workstations at the
conference site, prior to the presentation. During the oral presentation via telephone, visual
aids were presented by a local operator who provided realtime feedback to the presenter
via the Unix talk program.
Messy Futures and Global Brains
, Technical Report CCSR-94-26
Abtract: The recent history after WW-II was characterized by a relatively
simple partition of the world in basically two domains of superpower interests. Security
issues could be discussed and analyzed in global framework of two strategic players.
There were clear goals and roles for the players. Today with the role of strategic nuclear
weapons greatly reduced we have regional crises which have some similarities with
pre WW-I situations with one major difference: Today's world is much more connected,
especially information-wise: On a large scale we are able to get direct first hand information
from crisis areas and - for example through computer networks - can directly participate
in the discussion. That makes the future from a traditional control point of view messy
and on a global scale more complex and less predictable. For that reason we think that the
conditions for the emergence of a Global Brain will become a practical reality
for global modeling and simulation in the very near future. We also discuss some of the
potential future applications.
U. Dierker, M. Dueweke, A. Hübler,
Self-Assembling Electrical Connections Based on the Principle of Minimum Resistance
, Technical Report CCSR-94-27
Abtract: We study self-constructing and self-repairing electrical connections
built by agglomeration of metallic particles between two electrodes. Our experiments
show that self-assembling electrical connections grow by building a chain of particles
between two electrodes immersed in a dielectric liquid. We find that the growth time for
the self-assembling process is a linear function of the initial average spacing of metallic
particles and a linear function of the distance between the electrodes. Furthermore, the
experiments demonstrate the ability of the electrical connection to self-repair following
small pertubations. We discuss possible future applications of this phenomenon for fabricating
N. Birbaumer, W. Lutzenberger, H. Rau, G. Mayer-Kress, I. Choi, C. Braun,
Perception of Music and Dimensional Complexity of Brain Activity
, Technical Report CCSR-94-28
Abtract: The non-linear resonance hypothesis of music perception was tested
in an experiment comparing a group of musically sophisticated and a group of less sophisticated
subjects. The prediction that weakly chaotic music entrains less complex brain wave (EEG)
oscillations at the prefrontal cortex was confirmed by using a correlational dimension
algorithm. Strongly chaotic (stochastic) and periodic music both stimulated higher brain
wave complexity. More sophisticated subjects who prefer classical music showed higher
EEG dimensions while less sophisticated subjects responded with a drop in brain wave
complexity to rhythmical weakly chaotic music. Subjects ratings of perceived complexity of
the musical pieces followed mathematical (objective) structure of the music and did not reflect
the changes in brain wave complexity. The results are interpreted in the context of an associated
(Hebbian) network theory of non-linear brain dynamics.
P. Jung, G. Mayer-Kress,
Spatio-Temporal Stochastic Resonance in Excitable Media
, Technical Report CCSR-94-29
Abtract: We consider a two-dimensional pulse-coupled array of noisy threshold
elements with a long-range interaction. It is shown that the synchronization of activation
patterns with external excitatory waves shows a sharp peak at a finite, well-defined noise
level. This effect can be understood as a generalization of the concept of stochastic resonance
to spatially extended systems. We further show the impact of spatio-temporal stochastic
resonance for the spreading of spiral waves, where the noise level controls the scale and
size of the spiral.
P. Jung, B.J. Berne,
The Theory of Multi-Barrier Crossing
, Technical Report CCSR-94-30
Abtract: We investigate hopping in periodic potentials. In the limit of small
damping, multiple barrier crossing, i.e. hopping between nonadjacent potential wells,
becomes important. It is shown that these multiple hopping rates can be obtained systematically
in terms of the lowest lying band of eigenvalues of the Fokker-Planck equation. We study
multiple jump rates as well as jump-length distributions from strong to weak friction.
G. Mayer-Kress, P. Diehl, H. Arrow,
The United Nations and Conflict Management in a Complex World
, Technical Report CCSR-94-31
Abtract: We created a hyper-text document as part of an experiment to use
an evolving electronic document as reference and analysis tool with links to issues related
to United Nations and Conflict Management focussing on the example of the Balkan crisis.
It is intended to be intrinsically dynamic and multi-dimensional. The links to other documents
and data will continuously change and evolve, reflecting the ongoing developments in
the world. We want to see this as a conceptual modeling exercise, where the global computer
network is used as a tool without limiting ourself to formal and/or quantitative models.
It is a goal, however, to create links to quantitative models and data wherever appropriate.
For this paper itself we have only used material and resources that were obtained via the
We supplement the hyper-text pages with diagrams that should help in clustering
and connecting various elements of this complex structure and give a graphical representation
of relationships among the different sub-items. The links in those diagrams should be interpreted
very generally, not necessary implying specific causal or quantitative relationships unless
The paradigm that we want to use is that of a Global Brain: Instead
of engineering wiring diagrams or blueprints with well defined and structured pathways a
more adequate representation of a global system is that of neural connections in the brain.
They mainly facilitate associations between different nodes which then will be enhanced or
reduced according to their previous activation in relation to solving specific problems. Since
these diagrams and linked-networks are electronically accessible and easily modifiable, they
will not be static but maybe duplicated and modified according to different perspectives which
can compete among each others. An efficient selection mechanism based on adaptive and distributed s
imulations with short-term predictions can be expected to emerge.
Nonlinear Resonances: An Overview
, Technical Report CCSR-94-32
Abtract: Es wird gezeigt, dass der Response nichtlinearer Oszillatoren auf eine spezielle
Klasse aperiodischer Antriebskräfte gross ist. Diese speziellen Antriebskräfte werden nichtlineare
resonante Antriebskräfte genannt. Sie resultieren aus einer Minimierung des Antriebsaufwands
bei festgehaltener Endenergie und sind durch die zeitreflektierte Transiente der ungestörten
Dynamik des Oszillators gegeben (Prinzip des dynamischen Schlüssels
). Ein analytischer Beweis dieses Prinzips wird vorgestellt. Zur numerischen Verifikation der
analytischen Ergebnisse werden die Energietransfers bei sinusförmig und optimal getriebenen
Oszillatoren verglichen. Es zeigt sich, dass optimale Antriebskräfte dann besonders wirkungsvoll
gegenüber sinusförmigen sind, wenn die Dämpfung schwach und die Nichtlinearität hoch ist.
Weiterhin wurde festgestellt, dass optimale Antriebskräfte, die mit unterschiedlichen Normen für
den Antriebsaufwand errechnet werden, einander ähnlich sind. Eine Stabilitätsanalyse mit der
Multiple Scales - und der Strained Parameter - Methode für verschiedene
wichtige Systeme ergibt, dass die eingeführten optimalen Antriebe zu einer stanbilen Anregung führen. Die Untersuchung eines mehrdimensionalen Systems zeigt, dass es energetisch günstig ist, nur die am schwächsten gedämpfte Mode anzuregen. Unterliegt das System einem Rauschen, wird das Auftreten von
Stochastischer Resonanz beobachtet, d.h. der Response ist dann besonders gross,
wenn der Rauschanteil in der Antriebskraft ungefähr mit dem Rauschen im System übernimmt.
Technical Reports, with Abstracts: 1993
Global Information Systems and Nonlinear Methodologies in Crisis Management
, Technical Report CCSR-93-1 (January 1993)
Abtract: Crisis management can be seen as one of the major problems of a
sustainable development in the post-cold-war world order. Traditional approaches of
modelling, based on closed descriptions of more or less abstract global systems do not
appear to be adequate for the new challenges. We suggest that new evolutionary integrated
models will make extensive use of a rapidly growing global computer network that will
permit direct communication and efficient exchange of information as well as quantitative
and conceptual sub-models and simulations.
We present a very incomplete overview of
some of the information and modelling tools that are available today on the internet. We
discuss some recent experiences that we obtained by following the network discussions on
the current regional crises in the Balkans and how distributed integrated models on the
internet might help to prevent the violent escalation of future crises.
A. Hübler, D. Pines,
Prediction and Adaptation in an Evolving Chaotic Environment
, Technical Report CCSR-93-2
Abtract: We describe work in progress on computer simulations of adaptive
predicitve agents responding to an evolving chaotic environment and to one another. Our
simulations are designed to quantify adaptation and to explore co-adaptation for a simple
calculable model of a complex adaptive system. We first consider the ability of a single agent,
exposed to a chaotic environment, to model, control, and predict the future states of that
environment. We then introduce a second agent which, in attempting to model and control
both the chaotic environment and the first agent, modifies the extent to which that agent can
identify patterns and exercise control. The competition between the two predicitive agents can
lead either to chaos, or to metastable emergent behavior, best described as a leader-follower
relationship. Our results suggest a correlation between optimal adaptation, optimal complexity,
and emergent behavior, and provide preliminary support for the concept of optimal co-adaptation
near the edge of chaos.
E. Meiburg, N. Raju,
The Mixing Transition: Dynamical and Kinematic Consideration
, Technical Report CCSR-93-3
Abtract: Several aspects of the mixing transition for a plane three-dimensionally
evolving shear layer are studied using a subharmonically pertubed point vortex row. This
model mimicks the vortex pairing stage of the mixing layer evolution and is shown to give rise
to periodic, quasi-periodic, and chaotic particle trajectories and exponential interfacial
stretching rates. Particular attention focuses on the rapid production of small scales resulting
from the dynamics of the large-scale motion. We point out two distinct aspects of the transition
process, one being dynamical in origin, the other one purely kinematic. The dynamical aspects
are studied by analyzing the Poincare map and its stable and unstable manifolds, which provides
insight into the entrainment and detrainment of fluid into the mixing layer. The unstable manifold,
which acts as the organizing structure for the fluid transport processes, is visualized by computationally
tracking Lagrangian line elements in the model flow. The kinematic aspects of the transition are
studied by focusing on an isolated rotating vortex pair in a background strain field. For small
subharmonic pertubation amplitudes, a change in the topology of the streamline pattern in the rotating
reference frame leads to the formation of spiral arm structures seen in other work, and consequently to
a more intense production of small scales. For larger subharmonic pertubation amplitudes, this effect
does not occur. Hence strong subharmonic forcing does not lead to the more rapid production of small scales.
Qualitative comparisons with other models as well as experiments and direct Navier-Stokes simulations are discussed.
G. Mayer-Kress, I. Choi, N. Weber, R. Bargar, A. Hübler,
Musical Signals from Chua's Circuit
, Technical Report CCSR-93-4
Abtract: Chua's circuit can produce a very rich variety of signals, both periodic and
chaotic. We explore some classes of these attractors with respect to their auditory display and
musical properties. We discuss the fast control of the circuit through a specially developed
computer-controlled electronic resistor and how chaotic control methods might be applied
to optimally switch between different attractors. The Chua circuit has parameter regions
where noisy frequency and amplitude modulated sounds are generated, each of which is
related to a certain transition to chaos. We discovered a period-adding sequence of bassoon-like
sounds that produces interesting almost-harmonic pitch changes. Finally we emphasize the
importance of transient dynamics, especially in the context of percussion-like sounds.
D. Olson, A. Scheeline,
The Peroxidase/NADH Biochemical Oscillator: Experimental System, Control Variables, and Oxygen Mass Transport
, Technical Report CCSR-93-5
Abtract: Experimental control variables are defined and characterized to provide
good reproducibility of oscillatory behavior, and allow other investigators to perform additional
studies under consistently defined conditions. Fifteen variables are recognized and described.
Oxygen mass transport has a large effect on the overall appearance of the oscillations, and is
quantitatively related to stirring and several other variables. These conditions combine to yield a
single, experimentally measurable oxygen mass-transport constant. Stirring is controlled with a
precision motor which is used to explore the mass-transport constant and mixing time as a function
of stirrer rotation rate.
Oscillatory behavior is examined under identical conditions with and
without the modifiers methylene blue and 2,4-dichlorophenol (DCP). Omission of DCP from the system
does not appreciably change oscillatory behavior under the specified conditions. Slightly damped
oscillations are maintained for six hours. The acidic degradation of NADH is significantly affected by
illumination from the deuterium lamp used in UV-VIS absorption measurements.
and value of an analytical approach to this complex system is emphasized throughout.
Global Network Information Systems and Nonlinear Methodologies in Crisis Management
, Technical Report CCSR-93-6 (July 1993)
Abtract: Crisis management can be seen as one of the major problems of with regional
conflicts in the post-cold-war world order. Traditional approaches of modelling, based on closed
descriptions of more or less abstract global systems do not appear to be adequate for the new
challenges. We suggest that new evolutionary integrated models will make extensive use of a rapidly
growing global computer network that will permit direct communication and efficient exchange of
information as well as quantitative and conceptual sub-models and simulations. We would like to
point out analogies to mental processes in individual problem solving strategies and therefore
suggest the notion of a "Global Brain".
We present a very incomplete overview over some
of the information and modelling tools that are available today on the internet. We discuss in
the context of the current Balkan crisis how distributed integrated models on the internet might
help to develop general strategies for an improved management of future crises.
Hannay-Berry Phase and the Restricted Three Vortex Problem
, Technical Report CCSR-93-7
Abtract: Asymptotic expansions for the Hannay-Berry phase are computed for
a class of Hamiltonian systems in pertubed action-angle form with slowly varying parameters,
where the parameters recur on a slow time scale. A multi-scale pertubation method is used
which in principal can be carried to any desired order of accuracy. As a specific application,
we use the method to examine the restricted three vortex problem of two co-rotating point
vortices a distance D apart, and a tracer particle rotating around one of the vortices
with distance r. In the asymptotic limit r⁄D
≈ ε, we compute the particle trajectory through 0(ε) and find that
the Hannay-Berry phase is given by Δθ ≈ -7π-13⁄3 R0⁄
D sinh(4π)+0(1⁄D2) where R0 is
the conserved action. Reprint
Basic Research - Quo Vadis? The Grossmann - Committee is Giving its Recommendations
, Technical Report CCSR-93-8
Abtract: Life sciences, clinical and environmental research should receive
a significant amount of support from the Federal Minister for Research and Technology
according to an advisory committee. During the next few years some areas of physics will
have to rely on equipment already available.
Perspectives and Growth Areas of Basic Research in Germany
, Technical Report CCSR-93-9
Abtract: Basic research is no longer confined just to ivory towers and is no
longer confined to just a few interested people. The money which is spent for basic research is
tremendous. The annual budget of the German National Science Foundation (DFG) is larger
than 1.5 Billion DM (1 Billion US Dollar). The support for the Max-Planck-Gesellschaft (MPG)
is on the same level (1.2 Billion DM). The German Federal Ministry for Science and Technology
(BMFT) spends more than 3.5 Billion DM for basic research, which equals about 40 % of its annual
budget (these numbers include the BMFT share for the MPG). Of course, the basic research budget of
universities and industrial laboratories is on top of all that. In Germany more than 19 % of all the money
which is spent for research and development is spent for basic research whereas in Japan this ration
is 13 % and in the USA only 12 %. This article gives a detailed overview of major activities in basic
research in Germany and predictions on future developments.
G. Mayer-Kress, I. Choi, R. Bargar,
Sound Synthesis and Music Composition Using Chua's Oscillator
, Technical Report CCSR-93-10
Abtract: We describe simulations of Chua's oscillator and its implementation in
a circuit with seven computer-controlled parameters. We discuss its properties with regard
to sound synthesis and composition.
Can Chaos Be Symmetric?
, Technical Report CCSR-93-11
Abtract: If a system of ordinary differential (or difference) equations is invariant
under a diffeomorphism,
, that is
, for some integer
), any aperiodic solution is one of
distinct aperiodic solutions. In particular, any aperiodic solution of the Lorenz system, the
Chua oscillator, or the odd-logistic map is one of two aperiodic solutions; any aperiodic
solution of the Hénon-Heiles Hamiltonian system is one of three aperiodic solutions.
If their Ω-limit-sets are symmetric, they must be periodic. These mathematical results
do not necessarily relate to experimental observations or computer solutions. This illustrates
the dichotomy that can exist between mathematical concepts and the physical or computer
quantities with which they are associated.
P. McGuire, H. Bohr, C. Pershing, J. Rafelski,
Transitions to Volatility in Random Asymmetric Neural Networks
, Technical Report CCSR-93-12
Abtract: We numerically analyze the diversity of complex spatio-temporal
patterns of random asymmetric neural networks (RANNs) in synchronous, discrete time.
We study here the impact of noisy thresholds on network performance and find that there
is a narrow and interesting region of noise parameters where RANNs display a heretofore
unusual behavior desired for rapidly 'thinking' systems with a phase transition to a large
set of easily accessible states.
Technical Reports, with Abstracts: 1992
J. Breeden, N. Packard,
Model-Based Control of Nonlinear Systems
, Technical Report CCSR-92-1
Abtract: We show that model-based control of nonlinear systems without
feedback (open-loop control) can be obtained with many simple modelling procedures
rather than the globally defined ODE's normally assumed. We also extend this technique
to control from delay coordinate reconstructed state spaces. In the process, we find that
the appropriate choice of delay coordinates can be critical, since the stability of the
control is defined within the reconstructed state space.
B. Clarke, J. Mittenthal, M. Senn,
A Model for the Evolution of Networks of Genes
, Technical Report CCSR-92-2
Abtract: An organism persists through the activity of structural genes, which
is coordinated by clusters of coupled regulatory genes. During evolution, changes of coupling
within a cluster can increase the reliability with which its structural genes perform a task. To
study the evolution of coupling we have simulated and analyzed a stochastic model for a
simple problem. The assumptions of the model are these: A network of regulatory genes
coordinates the synthesis of four structural proteins, which associate in distinct heterodimers
that form a heterotetramer. Mutation in cis-regulatory regions produces transitions among 64 types
of network. In a population each network reproduces in proportion to its fitness, which depends
on its probability (reliability) of synthesizing the tetramer. Fitness-dependent attrition keeps
the size of the population constant. Regulatory genes occur in a sequence of levels; each level
is associated with a different family of transcription factors. The following results emerge:
Because different messengers within a family can give networks with the same connectivity,
the 64 types of networks cluster into 8 equivalence classes. During evolution with a low mutation
rate, high-fitness classes can be approached through various paths on a fitness landscape. With a
higher mutation rate networks remain preponderant. An initially homogeneous population
becomes more heterogeneous through mutation, but selection according to fitness later reduces
its diversity. During this process the entropy of the population increases, then decreases as the
population approaches a unique steady state.
A. Assad, N. Packard,
Emergent Colonizaton in an Artificial Ecology
, Technical Report CCSR-92-3
Abtract: This paper describes a computational model of organisms in an
artificial ecology where colonization emerges through a process of resource gathering
and exchange amongst an evolving population. Organismic fitness is defined implicitly
as a result of local interactions of the artificial organisms with each other and their environment,
with no explicit, global directive. The organisms move in the world, seeking different types
of resources, and they have the capacity to trade with each other, according to a genetically
encoded strategy. If the organisms can survive to the age of sexual maturity, they can reproduce,
and their offspring's strategy is changed using crossover and mutation of the parents' strategies.
The population is found to evolve a collection of strategies that tend to produce a spatial clustering
behavior which is observable at the population level, but is not explicitly specified anywhere in the
model. These clusters can be viewed as colonies since the organisms within them have actually
evolved to rely to a large extent on the coherence of the cluster as an efficient resource distribution
mechanism for their survival.
J. Mittenthal, B. Clarke, M. Levinthal,
, Technical Report CCSR-92-4
Abtract: The genome of an
cell contains codes for about 2000 different proteins. About half of these have now been
characterized to some extent. We can imagine that within the next 50 years the structures
and functions of every one of these proteins will have been determined and that the entire
genome will have been mapped in the greatest possible detail, so that we will know the exact
position of each E. coli gene, how the expression of each gene is regulated, and the exact chemical
nature of both the gene and its products. It will then be possible to write an
Encyclopedia of E. coli Life Processes
. If you were to ask someone the question "What is life?" and your respondent handed you the
Encyclopedia of E. coli Life Processes
, would you be satisfied?
Numerical Simulation of the Aligned Neutron Star Magnetosphere
, Technical Report CCSR-92-5
Abtract: For the case of aligned magnetic and rotational axes we solve a fluid
version of the Lorents-Dirac equation, in the Landau approximation, for a two-component
plasma. We start from an approximately force-free initial condition and numerically integrate
the full equations of motion for a time equal to 1.6% of one stellar rotation period. We find
that the system tends to a charge-separated state in which a negative charge region above
the poles is separated by a vacuum gap from a positive charge region near the equator.
We see the formation of force-free regions and a tendency of the vacuum gap to spread as
the integrations proceed. The energies attained by the charges are only mildly relativistic
and radiation reaction does not play an important role during the integrations. The negative
charge above the polar region is electrostatically bound and there is a force-free region
towards which the negative charge tends to flow. Some positive charge is magnetically
confined near the stellar equator and other positive charge crosses magnetic field lines
moving outward to the region beyond the light cylinder.
Optimal Representation of Experimental Data
, Technical Report CCSR-92-6
Abtract: No single state space reconstruction of experimental data is optimal
for all scientific endeavors. This thesis is all about the coordinates used in reconstruction,
the goals of reconstruction, and the criteria used to select optimal reconstructions. A
learning algorithm is described, which when given a space of possible coordinates and an
optimality criterion selects the best state space reconstruction. This method is applied to
specific problems: modeling nonuniformly sampled data, computing the inferable dimension
of a data set, and model-based control.
C. Kiankho Oei,
Walsh Function Analysis of Genetic Algorithms of Non-Binary Strings
, Technical Report CCSR-92-7
Abtract: The Walsh transform is used extensively as a tool in determining whether a
fitness function over a binary string is deceptive or not. This thesis shows that the Walsh transform
method for detecting deception is easily generalized to functions over non-binary strings such as
ternary strings, strings with real parameters, and strings with some binary and ternary characters and
some real parameters. A generalization of the Hadamard transform is then used to organize the generalized
Walsh coefficients into conditions for static deception for non-binary alphabets. The variances of fitness of
schemata are calculated using generalized Wals coefficients. Mathematica code for performing most of the
calculations mentioned is included.
Unreconstructible at Any Radius
, Technical Report CCSR-92-8
Abtract: Modeling pattern data series with cellular automata fails for a wide range of
deterministic nonlinear spatial processes. If the latter have finite spatially-local memory, reconstructed
cellular automata with infinite radius may be required. In some cases, even this is not adequate: an
irreducible stochasticity remains on the shortest time scales. The underlying problem is illustrated
and quantitatively analyzed using an alternative model class called cellular transducers.
P. Newton, S. Watanabe,
The Geometry of Nonlinear Schrödinger Standing Waves: Pure Power Nonlinearities
, Technical Report CCSR-92-9
Abtract: A numerical method to study radically symmetric standing wave solutions
(with arbitrarily large number of nodes) to the nonlinear Schrödinger equation is described and
used to study several new geometric features of these waves. The method is based on numerically
locating the basin boundary (separating surface) between two attracting invariant lines in phase
space. Each solution trajectory lies on the basin boundary, and is computed by 'squeezing' it between
two adjacent asymptotically stable trajectories. Of particular interest is the asymptotic distribution
of the eigenvalues and the conserved quantities which follow power law behavior. Also of interest
is the geometry of the basin boundary, which shows that the solution with a prescribed number
of zeroes is unique.
J. Breeden, N. Packard,
Computing the Inferable Dimension of a Data Set
, Technical Report CCSR-92-10
Abtract: We have developed a technique for computing the
of a time series di using a dynamical approach to distinguish dynamical variables
from random variables. di is the minimum number of dynamical variables necessary
to reproduce the observed data to within the noise envelope. This is different from calculations of
the minimum embedding dimension which use only topological considerations and thus compute
higher dimensions for higher noise levels. di also behaves well for short time series.
J. Breeden, N. Packard,
A Learning Algorithm for Optimal Representation of Experimental Data
, Technical Report CCSR-92-11
Abtract: We have developed a procedure for finding optimal representations of experimental
data. Criteria for optimality vary according to context; an
state space representation will be one that best suits one's stated goal for reconstruction. We consider a ∞-
dimensional set of possible reconstruction coordinate systems that include time delays, derivatives, and
many other possible coordinates; and any optimality criterion is specified as a real valued functional on
this space. We present a method for finding the maxima of the optimality function using a learning
algorithm based upon the genetic algorithm. The learning algorithm machinery for finding optimal
representations is independent of the definition of optimality, and thus provides a general tool useful
for a wide variety of contexts. Examples are given for chaotic model systems (Hénon, Mackey-Glass, etc.),
sunspots, pulsars, and cosmic ray muons.
Modeling and Control Systems: Paradigms and Applications
, Technical Report CCSR-92-12
Abtract: In many cases, the dynamics of high dimensional nonlinear systems can be
estimated from a low dimensional model. Nearly all variables are slaved by a few order parameters.
If the complex system is pertubed by an external force in order to control it or to investigate it
with a spectroscopic method, slaved variables can be stimulated and the prediction of the response
from the low dimensional model may be impossible. We show that it is generally possible to predict
the response of the complex system and to control it, if the external forces are resonant pertubations
of the low dimensional model. We present this issue in terms of a few paradigms including the
principle of the dynamical key, the principle of optimal interaction and the principle of matching in the
framework of other paradigms in complex systems research. We discuss open problems as well as
possible industrial applications.
J. Crutchfield, J. Hanson,
Attractor Vicinity Decay for a Cellular Automaton
, Technical Report CCSR-92-13
Abtract: We study the temporal decay of an attractor's vicinity for a domain-wall
dominated cellular automaton (CA). Using selected initial pattern ensembles, state space
structures in this high-dimensional nonlinear spatial system can be identified via the
resulting decay to its attractors. Considered over a range of lattice sizes, the decay behavior
falls into three main classes, each of which shows a characteristic profile. The first consists
of even-size lattices showing a decelerating decay to small nonattracted ensemble fractions.
The second class, also for even lattices, is a catastrophic decay to very small or vanishing
nonattracted fractions. The third class also shows catastrophic decay and contains all odd-size
lattices. Stochastic models are constructed that mimic the behavior of typical lattices throughout
their evolution until finite-size effects appear. Weak additive noise causes all states on all lattices
to fall into the attractor. In the end we find it overwhelmingly likely that the recently-proposed
attractor-basin portrait captures the CA's qualitative dynamics.
G. Mayer-Kress, R. Bargar, I. Choi,
Musical Structures in Data from Chaotic Attractors
, Technical Report CCSR-92-14
Abtract: One of the most prominent aspect of data from natural phenomena is that of
irregularity and complexity. Many universal aspects of such phenomena can be described in the
context of chaotic dynamics, and chaotic attractors can serve as model generators of such data.
Auditory representations used in conjunction with chaotic attractors can be designed to reveal the
unique properties of nonlinear dynamical systems representing complex phenomena. The design of
such an auditory representation can benefit from being informed by observations common to both
chaotic and musical structure. Recurrence structures in chaotic systems, including intermittency and
selfsimilarity, are compatible characteristics for drawing analogies to musical structures. In this paper
we explore several designs for auditory representation of chaotic systems. These include both low-level
methods (where the sequence of states of the system is mapped directly onto auditory parameters); and
higher-level methods which map derived statistical quantities, such as the approximations of the probability
distribution (measure) of an attractor into polyphonic auditory constructions. We focus on a few
simple dynamical systems where we have a clear understanding of the structure of chaotic attractors,
so that we can draw analogies between their representation using sound and the complex non-linguistic
structures found in music. Using these analogies we can develop a new generation of auditory
Chaos and Crises in International Systems
, Technical Report CCSR-92-15
Abtract: Nonlinear dynamical systems exhibit a very rich class of potential modes of
behavior. Among them are order, crises, and chaos, all of which can coexist within a very small
range of parameters. They may serve as paradigms for the complex new world order after the
end of the cold war where scenarios of delicate crisis management will replace those of
plain deterrence or retaliation.
In this note we first try to give a very short overview
of some basic elements of chaos theory. Then we discuss some work in relation to the
application of chaos theory to arms race dynamics. Finally we give an outlook of the potential
role of nonlinear dynamics and chaos in models for crisis management.
Testing for Nonlinearity in the EEG
, Technical Report CCSR-92-16
Abtract: Several normal human EEG recordings were tested for nonlinearity,
the necessary condition for deterministic chaos, using three different testing methods.
In all cases the tests failed to detect the nonlinear character of EEG dynamics. The explanation
by a linear stochastic process seems to be consistent with the EEG data.
M. Palus, V. Albrecht, I. Dvorák,
Information Theoretic Test for Nonlinearity in Time Series
, Technical Report CCSR-92-17
Abtract: A diagnostic test for identifying nonlinear dynamical relationships
in time series, based on mutual information and redundancy, functionals introduced
in information theory, is proposed. Its ability to distinguish (noised) multiperiodic and random
time series from time series generated by chaotic dynamical systems is demonstrated. The latter are
characterized by specific behaviour of marginal redundancies reflecting the increase of uncertainty
in time due to positive information production rate.
, Technical Report CCSR-92-18
Technical Reports, with Abstracts: 1991
T. Meyer, N. Packard, Local Forecasting of High Dimensional Chaotic Dynamics
, Technical Report CCSR-91-1
Abstract: We use a genetic learning algorithm to learn patterns in data produced
by a high dimensional chaotic attractor. The learned patterns are relationships between a region of the
attractor and the future behavior of orbits passing through this region. The learned patterns
give an accurate local profile of the attractor, and provide good forecasts.
P. Newton, Dynamics of Pertubed Amplitude Equations
, Technical Report CCSR-91-2
Abstract: The amplitude equation approach to hydrodynamic stability theory
typically leads to a hierarchy of equations which are solved independently at each order.
Implicit in this approach is the assumption that the higher order correction terms to the
equation have little effect on the dynamic properties of lower order solutions, i.e. the
assumption of structural stability. This is not always the case as will be demonstrated in two
model problems. The focus will be on 'correction' terms to the nonlinear Schrödinger equation,
in particular Ginzburg-Landau type pertubations arising in fluid dynamics and Zakharov type
pertubations arising in plasma physics. For
the Ginzburg-Landau equation, a two parameter singular limit will be described in which competing
stability mechanisms result in chaotic dynamics. For the Zakharov system, a certain kind of '
spikey' structure which develops on the plasma standing wave is captured using a multi-scale
pertubation method. This structure has been observed experimentally and plays an important
role in the modulational instability development.
A Learning Algorithm for Optimal Representations of Experimental Data
, Joseph. L. Breeden, Norman H. Packard, (See 92-11 for revised version), Technical Report CCSR-91-03
E. Atlee Jackson, A. Kodogeorgiou,
Entrainment and Migration Controls of Two-dimensional Maps
, Technical Report CCSR-91-04
Peter Grassberger, Thomas Meyer,
Forecasting Probabilities Using Neural Networks
, Technical Report CCSR-91-5
Complicated Dynamics and Controls in a Simple Economic Model
, Technical Report CCSR-91-06
J. E. Mittenthal, L.V. Beloussov,
Processes that May Shape Surfaces in Embryos
, Technical Report CCSR-91-07
Paul K. Newton, Shinya Watanabe,
The Geometry of Nonlinear Schr???dinger Standing Waves
, Technical Report CCSR-91-08
. Atlee Jackson, A. Kodogeorgiou,
A Coupled Lorenz-cell Model of Rayleigh-Benard Turbulence
(see 91-19 for revised version), Technical Report CCSR-91-09
Russel D. Shermer
Model-based Control of Spatially Extended Systems
(thesis), Technical Report CCSR-91-10
V. Thurner, W. Eberl, A. Hübler, N. Packard,
Determination of the Absolute Maximum of Polinomials by Algebraic Bisection Method
, Technical Report CCSR-91-11
Jay E. Mittenthal, Arthur B. Baskin, Robert E. Reinke,
Patterns of Structure and Their Evolution in the Organization of Organisms: Modules, Matching, and Compaction
, Technical Report CCSR-91-12 Reprint
Timothy L. Karr, Jay E. Mittenthal,
Adaptive Mechanisms that Accelerate Embryonic Developement in Drosophila
, Technical Report CCSR-91-13 Reprint
Arthur B. Baskin, Robert E. Reinke, Jay E. Mittenthal,
Exploring the Role of Finiteness in the Emergence of Structure
, Technical Report CCSR-9-14 Reprint
Joseph L. Breeden, Norman H. Packard,
Nonlinear Analysis of Data Sampled Nonuniformly in Time
, , Technical Report CCSR-91-15 Reprint
Paul K. Newton,
Rapidly Forced Initial Value Problems
, Technical Report CCSR-91-16 Reprint
Thomas P. Meyer,
Long Range Predictability of High Dimensional Chaotic Dynamics
(thesis), Technical Report CCSR-91-17 Reprint
Lenore Levine, Regular Language Invariance under One-dimensional Cellular Automaton Rules
, Technical Report CCSR-91-18 Reprint
E. Atlee Jackson, A. Kodogeorgiou, A coupled Lorenz-cell Model of Rayleigh-Benard Turbulence
, Technical Report CCSR-91-19 Reprint
Andrew Horner, David E. Goldberg, Genetic Algorithms and Computer-assisted Music Composition
, Technical Report CCSR-91-20 Reprint