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

TL;DR

This paper develops a mathematical framework for understanding how phase-locked states form and remain stable in synchronization models on Lie groups, extending previous work on Kuramoto and Lohe models.

Contribution

It introduces a new model of synchronization on Lie groups and analyzes the asymptotic formation and orbital stability of phase-locked states.

Findings

Framework for phase-locked state formation

Analysis of orbital stability on Lie groups

Extension of Kuramoto and Lohe models

Abstract

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).