A universal order parameter for synchrony in networks of limit cycle oscillators

Schröder, Malte; Timme, Marc; Witthaut, Dirk

doi:10.1063/1.4995963

Journal Article

FZJ-2017-05608

A universal order parameter for synchrony in networks of limit cycle oscillators

Schröder, M. (Corresponding author) ; Timme, M. ; Witthaut, D.FZJ*

2017
American Institute of Physics Woodbury, NY

Chaos 27(7), 073119 (2017) [10.1063/1.4995963]

This record in other databases:

Please use a persistent id in citations: http://hdl.handle.net/2128/18119 doi:10.1063/1.4995963

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.

Classification: