64 citations · 235 across the 17 of their papers we have counts for
22 papers
The shape of
Lee DeVille
We examine the graphs generated by the map for various , present some results on the structure of these graphs, and compute some very cool examples.
Dynamical systems defined on simplicial complexes: symmetries, conjugacies, and invariant subspaces
Eddie Nijholt, Lee DeVille
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicia…
Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
Lee DeVille
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 commo…
Synchronization conditions in the Kuramoto model and their relationship to seminorms
Jared C. Bronski, Thomas E. Carty, Lee DeVille
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical resu…
Circulant Type Formulas for the Eigenvalues of Linear Network Maps
Lee DeVille, Eddie Nijholt
Given an admissible map F for a homogeneous network N, it is known that the Jacobian DF(x) around a fully synchronous point x = (x0, ..., x0) is again an admissible map for N. Moti…
Runge-Kutta and Networks
Lee DeVille, Eugene Lerman, James Schmidt
We categorify the RK family of numerical integration methods (explicit and implicit). Namely we prove that if a pair of ODEs are related by an affine map then the corresponding dis…