Consensus on simplicial complexes: Results on stability and synchronization

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Abstract

We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian and show that it is a generalization of various consensus and synchronization models commonly studied on networks. In particular, our model allows us to formulate flows on simplices of any dimension so that it includes edge flows, triangle flows, etc. We show that the system can be represented as the gradient flow of an energy functional and use this to deduce the stability of various steady states of the model. Finally, we demonstrate that our model contains higher-dimensional analogs of structures seen in related network models.

Original languageEnglish (US)
Article number023137
JournalChaos
Volume31
Issue number2
DOIs
StatePublished - Feb 1 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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