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Stability of synchronization in simplicial complexes

Author

Listed:
  • L. V. Gambuzza

    (University of Catania)

  • F. Patti

    (CNR-Institute of Complex Systems)

  • L. Gallo

    (University of Catania
    INFN Sezione di Catania)

  • S. Lepri

    (CNR-Institute of Complex Systems)

  • M. Romance

    (University Rey Juan Carlos)

  • R. Criado

    (University Rey Juan Carlos)

  • M. Frasca

    (University of Catania
    Consiglio Nazionale delle Ricerche (IASI-CNR))

  • V. Latora

    (University of Catania
    INFN Sezione di Catania
    Queen Mary University of London
    The British Library)

  • S. Boccaletti

    (CNR-Institute of Complex Systems
    Northwestern Polytechnical University
    Moscow Institute of Physics and Technology
    Universidad Rey Juan Carlos)

Abstract

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

Suggested Citation

  • L. V. Gambuzza & F. Patti & L. Gallo & S. Lepri & M. Romance & R. Criado & M. Frasca & V. Latora & S. Boccaletti, 2021. "Stability of synchronization in simplicial complexes," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-21486-9
    DOI: 10.1038/s41467-021-21486-9
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