ReviewEntropy (Basel, Switzerland)2025
Synchronization of Kuromoto Oscillators on Simplicial Complexes: Hysteresis, Cluster Formation and Partial Synchronization.
Review in Entropy (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. Both partial and complete synchronization can be seen as quantified by the order parameter. The addition of interactions of a higher order than the usual pairwise ones can modify these features further, especially when the interactions tend to have the opposite signs. Cluster synchronization is seen on sparse lattices and depends on the spectral dimension and whether the networks are mixed, sparse or compact. Topological effects and the geometry of shared faces are important and affect the synchronization patterns. We identify and analyze factors, such as frustration, that lead to these effects. We note that these features can be observed in realistic systems such as nanomaterials and the brain connectome.
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