Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two?

Andreas Daffertshofer*, Robert Ton, Bastian Pietras, Morten L. Kringelbach, Gustavo Deco

*Corresponding author for this work

Research output: Contribution to JournalReview articleAcademicpeer-review


Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both.

Original languageEnglish
Pages (from-to)428-441
Number of pages14
Issue numberPart B
Early online date4 Apr 2018
Publication statusPublished - 15 Oct 2018


  • Criticality
  • Freeman model
  • Phase dynamics
  • Power laws
  • Synchronization
  • Wilson-Cowan model


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