Global Topological Synchronization on Simplicial and Cell Complexes

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Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However, the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures signals of any dimension can achieve global synchronization.
Original languageEnglish
Article number187401
Number of pages6
JournalPhysical review letters
Issue number18
Publication statusPublished - 3 May 2023


  • synchronisation
  • topological signals
  • collective behaviour
  • networks
  • dynamics on networks
  • coupled oscillators
  • simplicial complexes
  • cell complexes


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