64 citations · 235 across the 17 of their papers we have counts for
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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…
Configurational stability for the Kuramoto-Sakaguchi model
Jared Bronski, Thomas Carty, Lee DeVille
The Kuramoto--Sakaguchi model is a modification of the well-known Kuramoto model that adds a phase-lag paramater, or "frustration" to a network of phase-coupled oscillators. The Ku…
Synchronization and Stability for Quantum Kuramoto
Lee DeVille
We present and analyze a nonabelian version of the Kuramoto system, which we call the quantum Kuramoto system. We study the stability of several classes of special solutions to thi…