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000836502 1001_ $$0P:(DE-HGF)0$$aSchröder, Malte$$b0$$eCorresponding author
000836502 245__ $$aA universal order parameter for synchrony in networks of limit cycle oscillators
000836502 260__ $$aWoodbury, NY$$bAmerican Institute of Physics$$c2017
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000836502 520__ $$aWe analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously prove that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids.
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000836502 536__ $$0G:(HGF)VH-NG-1025_20112014$$aVH-NG-1025 - Helmholtz Young Investigators Group "Efficiency, Emergence and Economics of future supply networks" (VH-NG-1025_20112014)$$cVH-NG-1025_20112014$$x1
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000836502 7001_ $$0P:(DE-HGF)0$$aTimme, Marc$$b1
000836502 7001_ $$0P:(DE-Juel1)162277$$aWitthaut, Dirk$$b2
000836502 773__ $$0PERI:(DE-600)1472677-4$$a10.1063/1.4995963$$gVol. 27, no. 7, p. 073119 -$$n7$$p073119$$tChaos$$v27$$x1089-7682$$y2017
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