Kolloquiumsvortrag: Prof. Dr. Jürgen Kurths - Institute of Physics, Humboldt Universität zu Berlin / 11.01.16

11.01.2016 von 17:15 bis 18:45

Institut für Elektrotechnik und Informationstechnik, Kaiserstr. 2, 24143 Kiel, Geb. D Raum: "Aquarium"

Synchronization in Complex Networks and Its Stability: A Few Basics and some Applications



Synchronization phenomena are abundant in nature, science, engineering and social life, but it was first recognized by Christiaan Huygens in 1665 for coupled pendulum clocks; this was the beginning of nonlinear sciences. In the last two decades, this concept has been successfully extended to more complex systems, as the cardiovascular system or teleconnections in the climate system. Complex networks were firstly studied by Leonhard Euler in 1736 when he solved the Königsberger Brückenproblem. Recent research has revealed a rich and complicated network topology leading to interesting features of synchronization. Typical examples are the human brain, power grids, arrays of coupled lasers and the Amazon rainforest. A crucial problem is how stable synchronized regimes are in these systems against even large perturbations. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. This concept is applied to power grids, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. We mainly find that dead ends and dead trees strongly diminish stability. This will be discussed for the Northern European power system.


References: Pikovsky, A., M. Rosenblum, and J. Kurths, Synchronization – A Universal Concept in Nonlinear Sciences, Cambridge University Press 2001.

Arenas, A., A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Reports 2008, 469, 93. P. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physics 9, 89 (2013)

P. Menck, J. Heitzig, J. Kurths, and H. Schellnhuber, Nature Commun. 5, 3969 (2014)

P. Schultz, J. Heitzig, and J. Kurths, New Journal Physics 16, 125001 (2014)

Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Phys. Rev. Lett. 112, 114102 (2014)

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