The Cacophony of Interconnected Networks

  • Vitor H. P. LouzadaEmail author
  • Nuno A. M. Araújo
  • José S. AndradeJr.
  • Hans J. Herrmann
Part of the Understanding Complex Systems book series (UCS)


The harmony of an orchestra emerges from the individual effort of musicians towards mutual synchronization of their tempi. When the orchestra is split between two concert halls communicating via Internet, a time delay is imposed which might hinder synchronization. We present this type of system as two interconnected networks of oscillators with a time delay and analyze its dynamics as a function of the couplings and communication lag. We describe a breathing synchronization regime, namely, for a wide range of parameters, two groups emerge in the orchestra within the same concert hall playing at different tempi. Each group has a mirror in the other hall, one group is in phase and the other in anti-phase with their mirrors. For strong couplings, a phase shift between halls might occur. The implications of our findings on other interconnected systems are also discussed.


Interconnected Network Physarum Polycephalum Couple Network Functional Brain Network Kuramoto Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Authors would like to thank the Swiss National Science Foundation under contract 200021 126853, the CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil, the CNPq/FUNCAP Pronex grant, the ETH Zürich Risk Center, and the INCT-SC-Brasil for financial support. This work was also supported by grant number FP7-319968 of the European Research Council. NA acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) under Contract no. IF/00255/2013.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vitor H. P. Louzada
    • 1
    Email author
  • Nuno A. M. Araújo
    • 2
    • 3
  • José S. AndradeJr.
    • 1
    • 4
  • Hans J. Herrmann
    • 1
    • 4
  1. 1.Computational Physics, IfBETH ZürichZürichSwitzerland
  2. 2.Departamento de Física, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  3. 3.Centro de Física Teórica e ComputacionalUniversidade de LisboaLisboaPortugal
  4. 4.Departamento de FísicaUniversidade Federal do CearáFortalezaBrazil

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