Consensus on simplicial complexes: Results on stability and synchronization.

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.

• Publication year

  2020

• Venue

  Chaos

• Publication date

  2020-10-14

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1063/5.0037433arXiv 2010.07421PMID 33653041
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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