Countless processes and structures in our natural and technical environment can be regarded as networks. On a large scale as well as on a small scale, they are based on the idea that similar elements are interconnected in a complicated way. These interconnections are usually redundant, so there are several or a multitude of possible connections between two nodes. The dynamics of oscillatory networks dominate both natural and technological systems, including neural and genetic control loops, communication networks and AC power grids. Fail-safe functioning is essential for all these systems and depends on how such networks self-organize and react dynamically to external signals. For example, modern energy networks dynamically respond to predictable or stochastic perturbations, e.g. fluctuating feed-in power from renewable energy sources, changes in consumer behaviour, electricity trading or infrastructure failures. They all cause fluctuations in the grid frequency in a non-trivial, distributed manner.

However, how all units in a network collectively respond to such fluctuating inputs has not been well understood so far. In the recently published study, the research team presents a theory of dynamic response patterns in such networks and shows how distributed resonance patterns arise in oscillatory networks. The senior author of the study, Prof. Marc Timme from the Chair of Network Dynamics at cfaed says: “The network resonances are topology-specific, i.e. dependent on the exact structure of the connections between nodes in the network. They occur at medium frequencies of the input signals, between global but homogeneous reactions at low frequencies and localized reactions at high frequencies.”

This analysis shows why these special patterns occur and where they are most prominent in the network. These results can thus provide general theoretical insights into how fluctuating signals cause reaction patterns in networked systems and at the same time contribute to the development of practical guiding principles for the design and control of networks in practice. Xiaozhu Zhang, post-doctoral researcher and first author of the study, emphasizes the value of the results for practice: “In the example of AC power grids, this means that it is now possible to predict what kind of external disturbances could lead to dangerous responses in the network and where those responses may occur. In the worst case such resonant responses could result in a blackout. With this knowledge, network structures and control can be optimized to reduce this risk.”

• Paper: "Fluctuation-induced Distributed Resonances in Oscillatory Networks";
• Authors: Xiaozhu Zhang, Sarah Hallerberg, Moritz Matthiae, Dirk Witthaut, Marc Timme
• Journal: Science Advances; Release 31 July 2019; Open Access
• DOI: 10.1126/sciadv.aav1027
• Link: https://advances.sciencemag.org/content/5/7/eaav1027

Participating institutions:

• Chair of Network Dynamics, Institute for Theoretical Physics + Center for Advancing Electronics Dresden (cfaed), TU Dresden;
• Faculty of Engineering and Computer Science, Hamburg University of Applied Sciences;
• Institute for Energy and Climate Research - Systems Analysis and Technology Evaluation (IEK-STE), Forschungszentrum Jülich
• Institute for Theoretical Physics, University of Cologne;
• Department of Physics, Darmstadt University of Technology

Press graphic: Full resolution download: https://bit.ly/2yrIrk0

Image caption: Generality of response patterns. For two exemplary networks, the response patterns for three sinusoidal signals of low, intermediate and high frequencies representing the three response regimes are indicated by their relative response strengths (color coded). Both response patterns, in a random tree (upper row), and in the topology of the British high-voltage transmission grid (lower row), are reordered according to graph-theoretic distance from site of driven unit. For both networks, the driven unit is placed at the center with all units displayed on circles with their radii proportional to topological distance (gray concentric rings in the lower row).

Press contact: TU Dresden, Center for Advancing Electronics Dresden:

Prof. Marc Timme
Strategic Professorship for Network Dynamics
Phone: +49 (0)351 463-33846
E-mail: marc.timme@tu-dresden.de

Matthias Hahndorf
cfaed, Head of Public Relations
Phone: +49 (0)351 463 42847
E-mail: matthias.hahndorf@tu-dresden.de