  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 analogues of structures
seen in related network models.
