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A unified framework for simplicial Kuramoto models.

Marco Nurisso1,2,3, Alexis Arnaudon4, Maxime Lucas1

  • 1CENTAI Institute, Turin 10138, Italy.

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Summary
This summary is machine-generated.

This study unifies simplicial Kuramoto models, revealing their connection to standard Kuramoto models and exploring synchronization properties. Simple models show promise for reconstructing brain connectivity.

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Area of Science:

  • Complex Systems
  • Network Science
  • Mathematical Physics

Background:

  • Simplicial Kuramoto models extend traditional oscillator network analysis to higher-order structures (simplices).
  • Existing models are diverse, lacking a unified framework for systematic study.
  • Understanding synchronization in these complex systems is crucial for applications.

Purpose of the Study:

  • To present a unified framework for diverse simplicial Kuramoto models.
  • To analyze their properties using topology, discrete differential geometry, and gradient systems.
  • To explore their application in reconstructing brain functional connectivity.

Main Methods:

  • Categorization of models into "simple", "Hodge-coupled", and "order-coupled" (Dirac) groups.
  • Utilizing topology and discrete differential geometry for analysis.
  • Deriving bounds for simplicial synchronization and analyzing controllability.

Main Results:

  • Established an equivalence between simple simplicial Kuramoto models and standard Kuramoto models on pairwise networks.
  • Derived necessary and sufficient coupling strength bounds for simplicial synchronization.
  • Demonstrated competitive or superior performance of simple edge-based models in reconstructing brain connectivity.

Conclusions:

  • The unified framework facilitates systematic analysis of simplicial Kuramoto models.
  • Simple simplicial Kuramoto models offer a promising approach for network reconstruction, particularly in neuroscience.
  • Further research can explore controllability and applications in complex systems.