Deciphering the imprint of topology on nonlinear dynamical network stability

J. Nitzbon, P. Schultz, J. Heitzig, J. Kurths, F. Hellmann

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34 Citations (Scopus)
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Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrized to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields.
Original languageEnglish
Article number033029
Pages (from-to)1-15
Number of pages15
JournalNew Journal of Physics
Early online date27 Feb 2017
Publication statusPublished - 16 Mar 2017

Bibliographical note

The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The publication of this article was funded by the Open Access Fund of the Leibniz Association. We further thank Peng Ji for helpful discussions regarding the interpretation of the results.


  • coupled ocscillator networks
  • network stability
  • network topology
  • power grids
  • basin stability
  • survivability
  • second-order Kuramoto model


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