Network Dynamics
Head of group: Timme, MarcWe aim towards a fundamental understanding of the structure and dynamics of complex networks in physics and biology as well as engineered and social networks. We focus on computation in and control of networked systems, particularly neural circuits and power grids; moreover, the inference of network structures as well as their optimal design constitute basic research questions. We often develop mathematical tools required for understanding these highly complex systems. The Network Dynamics team works on foundations and applications in the areas of computational neuroscience, computer science, statistical physics of disordered systems, artificial neural networks and robotics, and, more recently, gene evolution and power grids and, most recently, complex human interaction networks.
Projects:

Dynamics of Modern Power GridsSwitching 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.
Socalled '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 nonlocal 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 coarsescale 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 (shorttime) regime.


Control and Selforganization for Autonomous RobotsHow 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 selforganized


Complex call sequences in social whale communicationHow do social animals communicate? Social whales may be one of the best fit animal model to study complex vocal communication patterns. We are interested in developing an automated classification system for vocalizations of killer whales and pilot whales. Very loosely speaking one can think of this as developing a "speech"recognition system for whale vocalizations. Another, more general aim of this project is to characterize whale vocalizations in terms of information theoretic measures and to compare them to human languages.


Structure, Dynamics and Function of Complex NetworksHow 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.


Complex Disordered Systems: Statistical Physics and Symbolic ComputationMany 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 antiferromagnetically 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.


Nonlinear Methods for Detecting Timing Relations in Neural DataMaking 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.


Theory of Precise Timing in Spiking Neural NetworksCoordinated 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.

People working in this Group: