论文标题
对简单络合物的共识，或：非线性简单laplacian
Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
论文作者
论文摘要
我们考虑了与简单laplacian相关的简单复合物上的非线性流，并表明它是对网络上常见研究的各种共识和同步模型的概括。特别是，我们的模型使我们能够在任何维度的简单上制定流，从而包括边缘流，三角流等等。我们证明该系统可以表示为能量功能的梯度流，并使用它来推导模型的各种稳态的稳定性。最后，我们证明我们的模型包含相关网络模型中看到的结构的较高维度类似物。
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.
