Consensus on simplicial complexes: Results on stability and synchronization
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Updated: Nov 15, 2025

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
1Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801, USA.
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.
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