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Seminar: The Role of Symmetries in Dynamical Networks - Summer Term 2014

Seminar: The Role of Symmetries in Dynamical Networks
Summer Term 2014

Ort: EW 731 (PN 731)

Zeit: Tuesday, 16:00 (s.t.)

The seminar offers perspectives on current research of the working group Schöll and the junior research group Hövel in the area Nonlinear Dynamics and Control. 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 case of interest on a particular topic, please contact the respective advisor. The final assignment of the topics will be done on April 15, 2014. The talks can be given in English or German.

Spontaneous symmetry-breaking in a complex dynamical system is a universal phenomenon which can occur in diverse fields such as physics, chemistry or biology. It means that processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. The role of symmetries in the dynamics of complex networks is the focus of the seminar. The seminar will give an overview of currently studied symmetry-breaking phenomena such as chimera states, partial amplitude death, oscillation death. Moreover, the analytical basic principles behind symmetries will be discussed as well as the connection between network symmetry and synchronization.

The seminar is generously supported by the G-RISC program in cooperation with the working group Fradkov (Saint-Petersburg State University, Russia). References for the preparation of the talks are given after every topic title.

The Role of Symmetries in Dynamical Networks



Vorbesprechung und Einführung
E. Schöll, A. Zakharova, P. Hövel

Symmetry breaking in networks: amplitude and oscillation death [ULL07, KOS10, KOS13]
Gustav Geißler

Sonderseminar - Chimera unchained [SET13, SET14]
Gautam C. Sethia

Sonderseminar - Control in machine learning
Markus Abel


Sonderseminar - Equivariant Pyragas control
Isabelle Schneider


Introduction to chimera states [KUR02a, ABR04]
Benedikt Hartung

Experiments on chimera states [HAG12, TIN12, MAR13, LAR13]
Iryna Omelchenko

Excitation waves on a minimal small-world model 
Benedikt Hartung

Chimera death: a bridge between chimera states and oscillation death [ZAK14]
Anna Zhakarova

Relating graph symmetries to the eigenvalue spectrum of network adjacency matrces [MAC09a]
Carolin Wille

Symmetry-breaking oscillation death in coupled tunnel diodes
Annika Stuke

Partial synchronization and partial amplitude death in mesoscale motifs of Stuart-Landau networks
Winnie Poel
Talks marked by * are suitable for students who want to obtain a “Seminarschein”.

The presentations are available online at "Seminardokumentationen". Login and password will be announced in the seminar and can be inquired at .


  • [ABR04] D. M. Abrams and S. H. Strogatz: Chimera states for coupled oscillators, Phys. Rev. Lett. 93, 174102 (2004)
  • [ATA03a] F. M. Atay: Total and partial amplitude death in networks of diffusively coupled oscillators, Physica D 183, 1--18 (2003)
  • [CAK14] C. Cakan, J. Lehnert, and E. Schöll: Heterogeneous delays in neural networks, Eur. Phys. J. B, accepted (2014), arXiv:1311.1919
  • [CLE13] E. Clerkin, S. O'Brien, and A. Amann: Multi-stabilities and symmetry-broken one-colour and two-colour states in closely coupled single-mode lasers, arXiv: 1308.1850v (2013)
  • [HAG12] A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll: Experimental observation of chimeras in coupled-map lattices, Nature Physics 8, 658--661 (2012)
  • [KOS10] A. Koseska and J. Kurths: Topological structures enhance the presence of dynamical regimes in synthetic networks, Chaos 20, 045111 (2010)
  • [KOS13] A. Koseska, E. Volkov, and J. Kurths: Oscillation quenching mechanisms: Amplitude vs. oscillation death, Phys. Rep. 531, 173--199 (2013)
  • [KUR02a] Y. Kuramoto and D. Battogtokh: Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators., Nonlin. Phen. in Complex Sys. 5, 380--385 (2002)
  • [LAR13] L. Larger, B. Penkovsky, and Y. L. Maistrenko: Virtual chimera states for delayed-feedback systems, Phys. Rev. Lett. 111, 054103 (2013)
  • [MAC09a] B. D. MacArthur and R. J. Sanchez-Garcia: Spectral characteristics of network redundancy, Phys. Rev. E 80, 026117 (2009)
  • [MAR13] E. A. Martens, S. Thutupalli, A. Fourri\`ere, and O. Hallatschek: Chimera states in mechanical oscillator networks, Proc. Nat. Acad. Sciences 110, 10563 (2013)
  • [PEC14] L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, and R. Roy: Symmetries, cluster synchronization, and isolated desynchronization in complex networks, (2014), arxiv.org/abs/1309.6605
  • [SET14] G. C. Sethia and A. Sen: Chimera states: the existence criteria revisited, (2013), submitted, arxiv.org/abs/1312.2682
  • [SET13] G. C. Sethia, A. Sen, and G. L. Johnston: Amplitude-mediated chimera states, Phys. Rev. E 88, 042917 (2013)
  • [TIN12] M. R. Tinsley, S. Nkomo, and K. Showalter: Chimera and phase cluster states in populations of coupled chemical oscillators, Nature Physics 8, 662--665 (2012)
  • [ULL07] E. Ullner, A. Zaikin, E. Volkov, and J. Garcia-Ojalvo: Multistability and clustering in a population of synthetic genetic oscillators via phase-repulsive cell-to-cell communication, Phys. Rev. Lett. 99, 148103 (2007)
  • [ZAK14] A. Zakharova, M. Kapeller, and E. Schöll: Chimera death: Symmetry breaking in dynamical networks. arXiv:1402.0348 (2014), arXiv:1402.0348


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