This title appears in the Scientific Report :
2017
Please use the identifier:
http://hdl.handle.net/2128/18119 in citations.
Please use the identifier: http://dx.doi.org/10.1063/1.4995963 in citations.
A universal order parameter for synchrony in networks of limit cycle oscillators
A universal order parameter for synchrony in networks of limit cycle oscillators
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...
Saved in:
Personal Name(s): | Schröder, Malte (Corresponding author) |
---|---|
Timme, Marc / Witthaut, Dirk | |
Contributing Institute: |
Systemforschung und Technologische Entwicklung; IEK-STE |
Published in: | Chaos, 27 (2017) 7, S. 073119 |
Imprint: |
Woodbury, NY
American Institute of Physics
2017
|
DOI: |
10.1063/1.4995963 |
PubMed ID: |
28764398 |
Document Type: |
Journal Article |
Research Program: |
Kollektive Nichtlineare Dynamik Komplexer Stromnetze Helmholtz Young Investigators Group "Efficiency, Emergence and Economics of future supply networks" Assessment of Energy Systems – Addressing Issues of Energy Efficiency and Energy Security |
Link: |
Published on 2017-07-27. Available in OpenAccess from 2018-07-27. Published on 2017-07-27. Available in OpenAccess from 2018-07-27. Published on 2017-07-27. Available in OpenAccess from 2018-07-27. |
Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.1063/1.4995963 in citations.
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. |