Asymptotic formation and orbital stability of phase-locked states in Kuramoto--Lohe type synchronization models on Lie groups

Some mathematical models of synchronization, such as the Kuramoto model (1975) and its generalizations pioneered by Lohe (2009), are formulated as ordinary differential equations describing populations of particles on Lie groups with locally attractive interactions. We suggest a model of synchronization on Lie groups and present a framework to understand the formation of phase-locked states and their orbital stability. This is a sequel to a previous joint work with Ha and Ko (2017).