Switching our current energy supply to renewable sources poses one of the greatest technological and social challenges of humankind. A successful transition in particular requires an intelligent upgrade of the current electric power grid. So-called 'smart grids' may provide part of the solution by enabling the transmission of demand and supply information across the grid online, thereby adapting energy production and distribution, and thus aiming to control the entire grid. However, stable operation as well as failures on large scales already today are consequences of the collective dynamics of the power grid and are often caused by non-local mechanisms. We thus urgently need to understand the intrinsic network dynamics on the large scale to complement partial solutions of control engineering and to be able to develop efficient strategies for operating the future grid. We thus develop and analyze appropriate coarse-scale models of future power grids with an emphasis on increasingly distributed demand and supply. First results show several intriguing features. For instance, the addition of new transmission lines may *destabilize* power grid operation (via Braess paradox that we identified in oscillator networks). In addition, replacing the few large power plants by many small and distributed ones may stabilize grid operation, at least in the stationary (short-time) regime.

How can distributed or autonomous systems control themselves to function properly? We are developing a novel line of research: Advancing the theory of chaos control we strive to bring it to applications for making autonomous robots more versatile and more self-organized

In mesoscopic systems, conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We investigate the conductance of a purely classical chaotic system. Such a system with either fully chaotic or mixed phase space generically exhibits fractal conductance fluctuations. This might explain unexpected results of experiments on semiconductor quantum dots.

Particles as well as waves flowing through a weak disorder potential show surprising branching effects. This has most notably been observed in two-dimensional electron gases, but is a phenomenon of much wider applicability. We study the formation of the caustics responsible for the branching of the flow.

Coordinated patterns of precisely timed activity is a key ingredient for neural information processing. This project investigates the theoretical fundamentals underlying the mechanisms for generating precisely timed spikes in complex neural networks.

Many particles interacting nonlinearly often give rise to very complex behavior. This is true even for apparently simple systems, such as those in thermal equilibrium. For instance, particles with a spin that are anti-ferromagnetically coupled may give rise to positive ground state entropy, an exception to the third law of thermodynamics. Investigating such complex ground states immediately leads us to hard enumeration problems in graph theory and computer science. Here we try to understand basic features of complex macroscopic states and in parallel develop tools for analytically and computationally addressing large system with complex ground states and related graph theoretical problems.

Making sense of huge neural data sets that contain spikes as well as temporally more coarse information constitutes a challenging task of current research. This is even more so as. for instance, the number of units possible to recorded from simulataneously, increases at a rapid pace. In this project we are developing novel methods of nonlinear time series analysis to relate dynamical quantities of neural activity on different temporal and spatial scales. We currently focus on relating the often precisely timed occurrence of spikes to the temporal evolution of local field potentials and low frequency oscillations via modern phase analysis techniques.

The dynamics of Bose-Einstein condensates in leaky optical lattices is studied (in the mean field limit). For some critical values of the interatomic interaction strength, the current of atoms leaving the trap exhibits avalanches that follow a power-law distribution and indicate the existence of a novel phase transition.

T.B.D.

T.B.D.

T.B.D.

We study the influence of disorder on the pseudo-hermitian phase of (generalized) PT-symmetric systems.

Neural networks display characteristics of critical dynamics in the neural activities as theoretically predicted. The power-law statistics for the size of avalanches of neural activity was confirmed in real neurons, where the critical behavior is re-approached even after a substantial perturbation of the parameters of the system. These findings provide evidence for the presence of self-organized criticality (SOC). We study neural network models that exhibit power-law statistics with realistic synaptic mechanisms, such as synaptic depression.

The biological function of self-organized criticality is much less understood than the physical mechanisms behind this phenomenon. Critical dynamics seems beneficial to living beings and it is known to bring about optimal computational capabilities, optimal transmission and storage of information, and sensitivity to sensory stimuli. We are interested in the developmental aspects of motor behavior in animals which we study in biomorphic autonomous robots.

How does the interaction topology of a complex network control its dynamics? Can we infer information about how a network is connected from dynamics measurements only? We address theoretical and practical aspects of such questions using mathematical modeling studies for general network dynamical systems and neural networks in particular.

This project divided into two subgroups: 'Aging effects in selective attention' and 'Dynamic adaptation in decoding temporal information' that both develop computational models to explain effects in cognitive psychology in a more detailed way than usual psychological theories can. These models base on knowledge about biological processes and insights via abstract modeling in computational neuroscience yielding quantitative model predictions that can directly be tested in psychological experiments.