You are here: Home Research Transdisciplinary Concepts & Methods Research Research Areas NEONET

Complex Networks of Networks (NEONET)

Our main research interests are complex networks and complex synchronization phenomena and their applications in climatology, sustainability research, and engineering; a main intention of our work is a strong interaction of methodological developments with applications.

Speaker: Jürgen Kurths

Research background

The analysis of complex systems in terms of networks has recently become an important interdisciplinary topic, which provides a modern tool to study spatio-temporal data. Complex networks often have irregular topological structures, therefore, the statistical analysis of the complex wiring architecture reveals the underlying principles, which initiates a revival of network modeling, developing new models to mimic its genuine properties.

As systems, we currently focus on the reconstruction of climate networks by means of nonlinear time series analysis approaches, working closely with scientists from research domain I. We intend to provide a new approach to study the impact of extreme events such as El Niños, Monsoons or volcanic eruptions on the topology of climate networks, which will allow new insights into the stability of the climate system. Our method may also be valuable to illuminate differences in different climate states of earth's history, e.g. holocene, glacial and cretaceous, and to assess the impact of global warming on the stability of the climate system from a different perspective.

On the other hand, a very important issue in the study of complex systems is the interplay between structure and dynamics. Much attention has been devoted to study the emergence of collective dynamics in complex networks from the viewpoint of relating the propensity for dynamics on a network to the topology and local properties. In particular, one aspect of this interplay is synchronization. Synchronization of oscillators acting on the nodes is one of the widely studied dynamical behavior on complex networks. It has been shown that dynamical processes, like network synchronization, are strongly influenced by the structure of the topology of the underlying network.

Furthermore, in many realistic systems, the feedback of dynamics can reshape the network structures. In this regard, one needs to consider evolving networks under the external influences, for instances, the effect of noise on the system dynamics. In particular, we established collaborations with research domains 2 and 3 to study the complex dynamics of ecological and socio-economic systems. We plan to simulate scenarios for a climate change (global warming, changing water supply, increased weather extreme events etc.) and the impact of different human activities (e.g. fragmentation of habitats) by means of the complex networks' approaches.

Methods

We will pioneer the new science of networks of networks (NEONET) and develop new tools for the reconstruction, characterization, design, control, and adaptation of NEONET as well as study structure formation on evolving NEONET, such as collective behavior, clustering, synchronization, and especially stability. These new techniques will be applied first to special interacting subsystems, in particular of climate and paleoclimate in relation to tipping points, power grids, social metabolism, and climate change, but also multi-level policy- and decision-making in view of  socially transmitted behavioral patterns.

Research Highlights

Network divergence of extreme rainfall in South America.

Network divergence of extreme rainfall
synchronicity. Positive (negative) values indicate
sinks (sources) of the network, which are
interpreted as locations where extreme events
occur shortly after (before) they occur at many
other locations. Besides the climatological
insights such typical propagation pathways of
extreme events can be directly used to identify
regions where extreme events have high
predictability.

We have established a new concept for studying the climate system from a complex network perspective, the climate networks, to uncover and represent spatial patterns and interrelations within the climate system, such as teleconnections. Strong non-linearities, extreme events, and spike-like data behaviour requested the introduction of the concept of event synchronization to study the spatial characteristics of the synchronicity of, e.g., extreme rainfall during the Asian and South American monsoon seasons. Such climate networks have been used to study the temporal order of extreme weather conditions and to design prediction schemes (together with RD2). Novel similarity measures developed in the flagship time series analysis have paved the way for the reconstruction of climate networks from palaeoclimate data (lake sediments, ice cores, stalagmites, tree rings, etc.), leading to the new concept of palaeoclimate networks. This approach has been used to find a systematic strengthening (weakening) of the Asian Monsoon during warm (cold) phases in the past millennium. To be able to consider the interactions between separated systems with the novel concept of interacting networks of networks (NEONET), we have introduced new network measures for characterizing them.

 

Topological comparison of ensemble results with real-world networks.

Comparison of basin stability, synchronizability,
and regularity/randomness of complex networks.
S
mall-world behaviour is a trade-off between the
optimal topologies for high
basin stability and
high synchronizability.

Pushing stability research a major step forward, we have developed network basin stability, a global concept that is widely applicable, to overcome the problem that Lyapunov's traditional local approach to dynamic stability is not sufficient for many real world systems, including climatic tipping elements. This enabled us to solve a long-standing problem from network science on the structure of synchronizing networks, and by applying it to power grids to uncover specific topological configurations that threaten power grid stability. We have suggested a smart wiring strategy to improve power grid resilience against large perturbations.

In our studies on synchronization and consensus as special cases of collective behavior, we have used adaptive complex networks and found that topological change and local synchronization have opposite effects on synchronization, and their tradeoff should be considered in the design of, e.g., mobile device networks. We have also uncovered that an abrupt transition to synchronization in complex networks, called explosive synchronization, can go via clustering, leading to the new phenomenon of clustered explosive synchronization. Moreover we uncovered a mechanism for this phenomenon .

Publications

  • P. J. Menck, J. Heitzig, N. Marwan, J. Kurths: How basin stability complements the linear-stability paradigm, Nature Physics, 9(2), 89–92 (2013).
  • P. J. Menck, J. Heitzig, J. Kurths, H. J. Schellnhuber: How Dead Ends Undermine Power Grid Stability, Nature Communication, in press (2014).
  • P. Ji, T. K. DM. Peron, P. J. Menck, F. A. Rodrigues, J. Kurths: Cluster explosive synchronization in complex networks, Physical Review Letters, 110(21), 218701 (2013).
  • Y. Zou, T. Pereira, M. Small, Z. Liu, J. Kurths: Basin of Attraction Determines Hysteresis in Explosive Synchronization, Physical Review Letters 112, 114102 (2014).

Third party funded projects

CoNDyNet
Verbundvorhaben CoNDyNet: Stabilität, Effizienz und Risiken
September 2014 – August 2017, Funded by: BMBF, PTJ
Contact: Kurths, Jürgen
CoSy-CC2
Ansätze zum Verständnis der Ursachen und Auswirkungen vergangener, gegenwärtiger und künftiger Klimaveränderungen auf Basis der Theorie komplexer Systeme
March 2014 – February 2018, Funded by: BMBF, PT DLR
Contact: Donner, Reik
Extreme Events II
Propagation of Extreme Events in Spatially Extended Excitable Systems
January 2015 – December 2017, Funded by: VW-Stiftung
Contact: Kurths, Jürgen
GOTHAM-RD4
Globally Observed Teleconnections and their role and representation in Hierarchies of Atmospheric Models
August 2016 – July 2019, Funded by: BMBF, PT DLR
Contact: Donner, Reik
IRTG - RD4
International Research Trainig Group (IRTG): Dynamical Phenomena in Complex Networks: Fundamentals and Applications
October 2011 – March 2016, Funded by: DFG - Deutsche Forschungsgemeinschaft
Contact: Kurths, Jürgen
MALCOD
Machine Learning for Computational Dynamics
September 2015 – August 2017, Funded by: EU, H2020
Contact: Kurths, Jürgen
PPP Indien
Rate Dependent Bifurcation of Thermoacoustic Instability
January 2017 – December 2018, Funded by: DAAD - Deutscher Akademischer Austausch Dienst
Contact: Kurths, Jürgen
PPP Norwegen
Nichtlineare Charakterisierung spätholozäner Klimavariabilität
January 2016 – December 2017, Funded by: DAAD - Deutscher Akademischer Austausch Dienst
Contact: Donner, Reik

Document Actions