94 citations · 264 across the 34 of their papers we have counts for
5 papers · 1 filter
Spectral perturbation by rank one matrices
Jon Merzel, Jan Minac, Lyle Muller +2
Let be a matrix of size over an algebraically closed field and a monic polynomial of degree . In this article, we describe the necessary and sufficie…
Joins of circulant matrices
Jacqueline Doan, Jan Minac, Lyle Muller +2
We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant gra…
Equilibria in Kuramoto oscillator networks: An algebraic approach
Tung T. Nguyen, Roberto C. Budzinski, Jacqueline Doan +3
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions rema…
Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
Roberto C. Budzinski, Tung T. Nguyen, Jacqueline Doan +3
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductor…
An algebraic approach to the Kuramoto model
Lyle Muller, Ján Minác, Tung T. Nguyen
We study the Kuramoto model with attractive sine coupling. We introduce a complex-valued matrix formulation whose argument coincides with the original Kuramoto dynamics. We derive…