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AG Nichtlineare Dynamik in Komplexen NetzwerkenWS 20/21

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Important information

The seminar will take place online via zoom.

To enter the seminar room, follow this zoom link:

The first seminar will take place on November 3rd at 16:15.

Please register in ISIS to access the digital material.

Credit points: Those who want to give a talk on the selected topic and receive credit points must register for the seminar on SAP before the talk.

If you have any problems, please send a message to Dr. Everton Medeiros at .

Seminar: Critical transitions in complex networks - Winter Term 2020/21


LV-Nr. 3233 L 611 Nichtlineare Dynamik in komplexen Netzwerken

Prof. Dr. Anna Zakharova, PhD

Dr. Everton S. Medeiros

Time: Tuesday 16:00 (c.t.)

Room: ER 164

Begin: 3.11.20 Durch den Besuch der Veranstaltung mit Vortrag und Ausarbeitung können 4 ECTS Punkte erworben werden.

The seminar offers perspectives on our current research in the field of Nonlinear Dynamics in Complex Networks. The seminar is particularly suitable for BSc and MSc students looking for a final project. Students, who want to obtain a Seminarschein, are welcome as well.

In general, the normal functioning of complex systems relies on a variety of factors ranging from the internal conditions to the characteristics of the surrounding environment. Fortunately, the stabilization mechanisms of such systems prevent failures for mild changes in the underlying functioning conditions. However, systematic variations of such actuation parameters may bring complex systems to stability thresholds at which any further parameter change, or any small external disturbances, can cause the sudden collapse of the system’s normal behavior.
Such critical transitions may occur in a large variety of contexts. For example, in ecology, these transitions may imply the collapse of mutualistic relations among species. In climate dynamics, they can disrupt the Atlantic thermohaline circulation. In technological devices, the transitions may expose power-grids to regimes of high susceptibility to failures. In such a transdisciplinary scenario, the framework of dynamical systems combined with complex networks is usually applied to develop means for the detection, suppression, or at least, provide early-warning signals for critical transitions.
With this, in this seminar, we offer an overview of such critical transitions from the perspective of nonlinear systems addressing concepts such as local and global stability, bifurcations, multistability, chaos, control, among others. The available topics range from the critical functioning of the brain and explosive synchronization in multilayer networks to cascade failures in power-grids and tipping elements of the Earth’s climate. Moreover, the approaches among the proposed topics are diversified in lab experiments, mathematical models, and analysis of real-world data.

Schedule and Organization: If you are interested in a particular topic, please contact one of the advisors. Final assignment of the topics will be done on 03.11.2020.


Introduction and organization
AZ and EM
Investigating the Risk of Hurricane-Induced Cascading Failures in Power Systems of the U.S. East Coast
Julian Stürmer
Edges of inter-layer synchronization in a time switching double-layer network
Muhittin Eser

Explosive Synchronization in Adaptive and Multilayer Networks [ZHA15]
Iwan Phillips

Criticality in the brain: A synthesis of neurobiology, models and cognition [COC17]
Max Contreras

Network-induced multistability through lossy coupling and exotic solitary states [HEL20]
Leonhard Schülen

Rate-induced tipping in ecological systems
Anna Vanselow

The Functional Benefits of Criticality in the Cortex
Ben Böbel

Control of inter-layer synchronization by multiplexing noise [VAD20]
Leander Rolef

Low-dimensional dynamics of networks of stochastic spiking neurons
Bastian Pietras

2-Cluster Fixed-Point Analysis of Mean-Coupled Stuart-Landau Oscillators in the Center Manifold
Felix Kemeth


Recurrence properties of a spatially extended food-chain
Leonard Schulz

Predicting tipping points in mutualistic networks through dimension reduction [JIA18]
Jonah Friedrich

to be announced
Simona Olmi

Network dynamics of drought-induced tipping cascades in the Amazon rainforest
Nico Wunderling

Talks marked by • are suitable for students who want to obtain a “Seminarschein”.

If you are interested in a particular topic, please contact one of the advisors. Final assignment of the topics will be done on 03.11.2020.


AZ Prof. Dr. Anna Zakharova, PhD

EM Dr. Everton S. Medeiros
LS Leonhard Schülen, MSc
MC Maximiliano Contreras, MSc


[JIA18] Jiang J., Huang Z., Seager T. P., Lin W., Grebogi C., Hastings A. Lai Y-C., Predicting tipping points in mutualistic networks through dimension reduction. Proceedings of the National Academy of Sciences 115, E639 (2018)

[COC17] Cocchi L., Gollo L. L., Zalesky A., Breakspear M., Criticality in the brain: A synthesis of neurobiology, models and cognition. Progress in neurobiology 158, 132 (2017).

[HEL20] Hellmann F., Schultz P., Jaros P., Levchenko R. Kapitaniak T., Kurths J., Maistrenko Y., Network-induced multistability through lossy coupling and exotic solitary states. Nature Communications 11, 1 (2020)

[DAI12] Dai L., Vorselen D., Korolev K. S., Gore J., Generic Indicators for Loss of Resilience Before a Tipping Point Leading to Population Collapse. Science 336, 1175 (2012)

[WIL19] Wilting J., Priesemann V., Between Perfectly Critical and Fully Irregular: A Reverberating Model Captures and Predicts Cortical Spike Propagation. Cerebral Cortex 29, 2759 (2019)

[VAD20] Vadivasova T. E., Slepnev A. V., Zakharova A., Control of inter-layer synchronization by multiplexing noise. Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 091101 (2020)

[LEN11] Lenton T. M., Early warning of climate tipping points. Nature Climate Change 1, 201 (2011)

[EZA20] Ezaki T., Dos Reis E. F., Watanabe T., Sakaki M., Masuda N., Closer to critical resting-state neural dynamics in individuals with higher fluid intelligence. Communications biology 3, 1 (2020)

[BAP16] Baptista M. S., Szmoski R. M., Pereira R. F., de Souza Pinto S. E., Chaotic, informational and synchronous behaviour of multiplex networks. Scientific Reports 6, 22617 (2016)

[ZHA15] Zhang X., Boccaletti S., Guan S., Liu Z., Explosive Synchronization in Adaptive and Multilayer Networks. Phys. Rev. Lett. 114, 038701 (2015)

[BEG12] Beggs J. M., Timme N., Being critical of criticality in the brain. Frontiers in physiology 3, 163 (2012)

[SCH18] Schäfer B., Witthaut D., Timme M., Latora V. Dynamically induced cascading failures in power grids. Nature Communications 9, 1 (2018)



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