Higher-order sync

sync with group interactions

Synchronisation is a well-known phenomenon that plays a key role in physics, biology, and neuroscience, to cite a few. A typical example is when people in an audience clap in unison, because of their (audio and visual) interactions, or when heart cells synchronise to make the heart beat. A lot of theoretical work exists on synchronisation, but mostly considers pairwise interactions.

Evidence suggests, though, that higher-order interactions, i.e. between more than two units a time, are important to fully capture complex processes. To study this, we consider generalisations of the Kuramoto mode, where we include interactions terms between two or more oscilators.


  1. Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
    Y. Zhang,  P. S. Skardal,  F. Battiston,  G. Petri, and  M. Lucas
  2. A unified framework for Simplicial Kuramoto models
    M. Nurisso,  A. Arnaudon,  M. Lucas,  R. L. Peach,  P. Expert,  F. Vaccarino, and  G. Petri
  1. Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
    Y. Zhang*,  M. Lucas*, and  F. Battiston
    Nat. Commun., 2023
  2. Multiorder Laplacian for synchronization in higher-order networks
    M. Lucas,  G. Cencetti, and  F. Battiston
    Phys. Rev. Res., 2020
  3. Networks beyond pairwise interactions: structure and dynamics
    F. Battiston,  G. Cencetti,  I. Iacopini,  V. Latora,  M. Lucas,  A. Patania,  J.-G. Young, and  G. Petri
    Phys. Rep., 2020
Book chapters
  1. Multiorder Laplacian for Kuramoto Dynamics with Higher-Order Interactions
    M. Lucas,  G. Cencetti, and  F. Battiston
    In Higher-Order Systems, 2022