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Complex systems
S
ystems are composed of welldefined components that, when
integrated, act together to form a
functioning entity. Identifying a
system or a hierarchy of systems
requires a certain level of abstraction and
simplification. Simple systems have few
components, and their behaviour is fully
understandable and predictable. Consider a
ball falling through the air; this simple
system consists of the ball falling under the
influence of the gravitational force with a
viscous drag. Add more balls and this system
becomes complex: vortices from each ball
affect the fall of the other balls in a manner
that cannot be simply extrapolated from the
fall of a single ball.
Complex systems have many components that interact to create a functioning
unit without an overarching regulatory
body1. It is the self-organized cooperative interaction of the individual components that
determines the emergent functionalities.
From selF-organization to liFe
Complex self-organizing systems are prevalent in nature. They are part of our everyday
lives in areas ranging from ecology, sociology and economics, to biology, medicine,
chemistry and physics. Many systems share
similar spatio-temporal structures. For example, one might ask whether the large-scale periodic structure of sand dunes is related to the
nanoscale patterns of polymer microstructures, whether the turbulence is similar in
stars and in a stirred coffee cup or whether
cardiac fibrillation is related to the aggregation dynamics of social amoebae. It is remarkable that these statements are true.
Numerical simulation and advanced experimental tools now allow detailed quantitative investigations of the spatio-temporal
evolution of complex systems, including not
only spatially extended systems2, but also
highly coupled networks. This is well illustrated by the example of epidemic outbreaks
and the subsequent geographic spreading of
infectious disease, which incidentally mirrors the transportation of banknotes.
Higher organisms develop through the
collective organization of many cells. The
biological cells themselves are complex systems that use highly evolved genetic regulatory schemes to create structures that can dynamically maintain themselves or contribute
to a higher multicellular organism. These
regulatory schemes in turn integrate complementary types of information3. At both the
single-cell and multi-cell levels there remains
a fundamental challenge to understand the
principles behind the developmental process that lead to the formation of complex
patterns and morphologies4 (Fig. 1).
Complexity oF heart and mind
Among the organs of the human body, the
functions of the heart and the brain are
highly complex in that their operation
emerges from the collective dynamics of
millions of strongly interacting cells, which
are well organized in their geometrical
structure and connectivity. In heart muscle,
the propagation of a nonlinear wave pulse
— the cardiac action potential — controls
the contraction. Usually the propagation is
well organized and the heart functions as an
efficient biological pump. During cardiac
fibrillation, vortex-like rotating waves of
electrical activity result in spatio-temporal
chaotic excitation and contraction patterns5
(Fig. 2). This electro-mechanical malfunction
causes an estimated 738,000 deaths per year
in Europe alone. Yet the physical mechanisms
underlying the dynamics and control
continue to pose a fundamental scientific
riddle.
P
rediction and control of pandemics could be improved by complexsystems research at the max planck institute for dynamics and
self-organization. infected persons transport bacteria and viruses
across great distances, transmit them to others and spread the pandemic.
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Research Perspectives of the Max Planck Society | 2010+
Similarly, in the brain, the propagation
of a nonlinear wave pulse — namely, the
neural action potential — is the basis of its
computational and memory power. Here
the high degree of interconnectivity and
topological complexity of the neuronal
network results in the coordinated activity
of millions of interacting nerve cells that
comprise the human mind. The real-time
processing of inputs interacts with the
slower process of learning through activitydependent changes of synaptic response6,7.
The workings of the brain, however, cannot
be fully understood if viewed only as a
complex dynamical system. For example,
it is possible to describe the brain’s
processing of hierarchically structured
sequences (such as sentences) at the neuralsystems level as an initial phase of local
structure building, immediately followed
by a second phase of creating hierarchical
dependencies8. Therefore, understanding
the operation of the mind also requires
describing and analysing its emergent
information processing functions. This
specific ability to extract rules underlying
hierarchical dependencies appears to
differentiate humans from non-human
primates. Advances in many aspects of
neural computation have been addressed
by pattern formation, statistical inference
and optimal decision-making, borrowing
from the mathematical language of
statistical physics9.
Complex teChniCal systems
Complex-systems research also encompasses artificially created systems that are
changing the environment on a scale never
seen before. Can the Earth’s resources be
better utilized?
Humankind has made significant
progress in increasing the productivity, se-
researchers evaluated data from the popular banknote-tracking
website (www.wheresgeorge.com) and showed that a two-parameter
random-walk model can accurately describe human travelling behaviour
mathematically (Brockmann, D. et al. Nature 439, 462, 2006).
Chemistry, PhysiCs and teChnology
interactions of individual components in a system determine an overall
emergent functionality that does not independently exist.
Complex systems need energy to sustain their behaviour; minute changes
in one component can have consequences for the system as a whole.
theories must cover ranges of temporal or spatial scales, the interplay
between the individual history and universal features, and the selforganization of elements and of collective phenomena.
Fig. 1 | Tissue organization involves cellular compartments
separated by sharp interfaces.
Fig. 1, left image courtesy of Christian Dahmann, MPI-GPG. Fig.1, right image courtesy of Frank Jülicher, MPI-PKS . Fig. 2, images courtesy of Stefan Luther, MPI-DS.Turbulence photograph courtesy of Haitao Xu, MPI-DS.
In the fly wing (left image), two compartments are revealed by green-fluorescent
protein labelling of cells. Simulation of a compartment boundary (right image).
lectivity and sustainability of chemical and
biotechnological production processes. Moving forwards, further breakthroughs in process systems engineering are needed in order
to make the transition from fossil fuels and
petrochemical feed stocks to renewable materials and energy. Theoretical and experimental approaches need to be developed for
the analysis and design of chemical and
biochemical production systems, with a
focus on their inherent multilevel structure.
New technological and production processes based on complex-systems research promise to close carbon dioxide cycles, enhance
efficiency, and incorporate new functionality in materials and products10.
turbulent times
Turbulence manifests itself in myriad ways
across the physical, chemical, engineering
and even biological sciences. It occurs whenever fluid viscous forces are smaller than the
dominant driving forces of the flow; in
practice this includes most natural and technological flows11. Turbulence is a fundamental topic in fluid and dynamical systems
research that raises basic questions in both
applied mathematics and informatics.
The study of turbulence thus unites
many types of researcher, from earth scientists studying the terrestrial biosphere and
the exchange of heat, momentum and matter within the forest canopy, to physicists
exploring strategies for confining plasma in
experimental fusion reactors, and even
mathematicians developing fundamental
new numerical methods.
Advanced understanding of complex
systems will open new paths for translating
fundamental scientific into practical functions. It has applications in subject areas
ranging from life sciences and medicine,
physics, chemistry and engineering, to social, economic and cognitive sciences. The
challenge for scientists is to reconcile the differences and similarities, and the shared and
disparate features, across physical, biological
and chemical systems that are natural and
artificial.
➟ For references see pages 70 and 71
Fig. 2 | Cardiac fibrillation.
The images show spatial-temporal chaotic electric-excitation patterns on the surface
of heart tissue (field of view = 6 × 6 cm2). Black areas indicate resting tissue and yellow
areas indicate excited tissue. A lack of synchronization leads to failure of the heart as
a pump and sudden death (s, seconds).
1.144 s
1.154 s
1.184 s
left
The image shows
turbulence in clouds
at a height of 2,700 m
above sea level on the
Zugspizte mountain
at the border between
Austria and Germany. The
dynamics of particles (ice
or droplets) in turbulent
inhomogeneous flows
is essential for the
understanding of cloud
and rain formation.
Cloud dynamics are
largely responsible for the
uncertainty in climate
predictions.
2010+ | Research Perspectives of the Max Planck Society
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