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General Research Programme

The overarching goal of the Collaborative Research Center (CRC) 910 is to control dissipative structures
in nonlinear dynamical systems far from thermodynamic equilibrium. Such systems often exhibit self-
organization, i.e., the spontaneous emergence of temporal, spatial, or spatio-temporal structures from
the inherent nonlinear cooperative dynamics. Dissipative structures in self-organizing nonlinear systems
are widespread in physics, chemistry, and biology.


With this CRC we go beyond merely describing the intriguing dynamics of self-organizing nonlinear
systems: by combining an interdisciplinary team of applied mathematicians, theoretical physicists, and
computational neuroscientists we aim at developing novel theoretical approaches and methods of control,
and demonstrating the application of these concepts to a selection of innovative self-organizing systems
ranging from condensed hard and soft matter to biological systems. To meet these challenges, we are
merging and advancing concepts from the control of nonlinear dynamical systems, the classical mathe-
matical control and optimization theory, and coherent quantum control. Our focus is on theoretical and
methodological developments from a conceptual point of view (project group A) and with a perspective
on applications (project group B). Our key areas of application, which we have already opened up in
the first and second funding period, are quantum systems, soft condensed matter, and various types of
networks. In the third funding period we will, on the one hand, further strengthen the synergies and
collaborations in and between these fields. On the other hand, we introduce new foci such as control
of (classical) multilayer and chemical reaction networks, control of topological quantum information
processing, mathematical control of stochastic systems, and control of active and turbulent fluids. The
application of our concepts to concrete experiments will be fostered by specific external collaborations
of the individual projects.


Depending on the dynamical system considered, its control may target different aspects such as stabi-
lization of unstable steady states, periodic oscillations, or spatio-temporal patterns, suppression of chaos
(chaos control), design of the dynamics of a complex network, or control of the coherence and timescales
of noise-mediated motion. A particularly important concept in our CRC is feedback control (closed-loop
control), where unstable states are stabilized adaptively by using the internal dynamics of the system to
adjust the control force, rather than externally imposing a fixed value. A versatile example is provided
by time-delayed feedback control, where the control signal is constructed from some time-delayed out-
put variable of the system. Using algorithms of optimal control, the proposed control methods can be
optimized with respect to the forcing or feedback protocol in order to minimize, for example, the energy
5and the time needed to achieve control. A new issue in the third funding period will be optimal control
of stochastic mean-field systems and of reaction-diffusion systems for brain networks.


With research on quantum systems, soft condensed matter and networks we continue to study emerg-
ing fields of applications for control algorithms which have hitherto been mainly confined to classical
macroscopic systems. In the third funding period, new aspects in the field of networks will be multilayer
network models, power grids, and quantitative approaches to the reservoir computing performance of
optical networks. For quantum systems, a key challenge is to apply concepts of time-delayed feedback
to control nonlinear phenomena dominated by quantum fluctuations. In the third funding period we
will particularly focus on error corrections for quantum information processing, dissipation engineering
and on steering quantum interferences via a coherent self-feedback mechanism beyond classical Pyra-
gas control. Control of soft condensed matter in nonequilibrium such as driven colloidal suspensions
and flowing complex fluids is still a novel and innovative issue, challenges being the manipulation of
dynamical structures and transport on the particle scale, and the design of microfluidic patterns. New
topics here are the control of active fluids, which are intrinsically out of equilibrium, the dynamics under
time-delayed feedback, and the control of elastic turbulence. Further we will intensify research on the
control of cardiac tissue, an active medium with typically chaotic spatiotemporal dynamics, and on neural
systems, where inherent time-delayed and nonlocal feedbacks play an important role. Understanding and
designing corresponding control mechanisms may eventually lead to substantial progress in defibrillation
and the understanding of the impact of non-invasive brain stimulation on global brain activity.


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