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@ARTICLE{Schrder:836502,
      author       = {Schröder, Malte and Timme, Marc and Witthaut, Dirk},
      title        = {{A} universal order parameter for synchrony in networks of
                      limit cycle oscillators},
      journal      = {Chaos},
      volume       = {27},
      number       = {7},
      issn         = {1089-7682},
      address      = {Woodbury, NY},
      publisher    = {American Institute of Physics},
      reportid     = {FZJ-2017-05608},
      pages        = {073119},
      year         = {2017},
      abstract     = {We analyze the properties of order parameters measuring
                      synchronization and phase locking in complex oscillator
                      networks. First, we review network order parameters
                      previously introduced and reveal several shortcomings: none
                      of the introduced order parameters capture all transitions
                      from incoherence over phase locking to full synchrony for
                      arbitrary, finite networks. We then introduce an
                      alternative, universal order parameter that accurately
                      tracks the degree of partial phase locking and
                      synchronization, adapting the traditional definition to
                      account for the network topology and its influence on the
                      phase coherence of the oscillators. We rigorously prove that
                      this order parameter is strictly monotonously increasing
                      with the coupling strength in the phase locked state,
                      directly reflecting the dynamic stability of the network.
                      Furthermore, it indicates the onset of full phase locking by
                      a diverging slope at the critical coupling strength. The
                      order parameter may find applications across systems where
                      different types of synchrony are possible, including
                      biological networks and power grids.},
      cin          = {IEK-STE},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {153 - Assessment of Energy Systems – Addressing Issues of
                      Energy Efficiency and Energy Security (POF3-153) /
                      VH-NG-1025 - Helmholtz Young Investigators Group
                      "Efficiency, Emergence and Economics of future supply
                      networks" $(VH-NG-1025_20112014)$ / CoNDyNet - Kollektive
                      Nichtlineare Dynamik Komplexer Stromnetze $(PIK_082017)$},
      pid          = {G:(DE-HGF)POF3-153 / $G:(HGF)VH-NG-1025_20112014$ /
                      $G:(Grant)PIK_082017$},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000406762000021},
      pubmed       = {pmid:28764398},
      doi          = {10.1063/1.4995963},
      url          = {https://juser.fz-juelich.de/record/836502},
}