The network Kuramoto model is a celebrated model of coupled oscillators renowned for the complex self-organizational synchronization behaviour it exhibits with relatively simple dynamics. Much work has been done in the dynamical systems and control communities on predicting which model parameters lead to synchronization and which do not. I will be presenting an established method due to Dorfler, Chertkov, and Bullo for bounding the bifurcation point from above, my own variation on the method for bounding the bifurcation from below, a reformulation of partial synchronization predictions as a graph theoretical optimization problem, and will connect the questions we have about the Kuramoto model to well-studied questions in spectral graph theory and power engineering.
Brady Gilg is PhD candidate in Applied Mathematics at Arizona State University. Under Professor Dieter Armbruster, he is researching synchronization phenomena in dynamical networks of phase oscillators. Previously, Brady completed national merit-sponsored bachelor's degrees in computational math and physics from ASU with abroad studies at the University of Nebraska and the University of Queensland. Additionally, Brady has researched magnetic sensing for the physics department of UNL and most recently participated in the multinational GRIPS program in Berlin, Germany sponsored by the Institute for Pure and Applied Mathematics.