Stability and Synchronization of Kuramoto Oscillators

TL;DR

This paper investigates the stability and synchronization phenomena in Kuramoto oscillators, providing graph-theoretic criteria and experimental insights into their collective behavior across various physical systems.

Contribution

It introduces graph-based stability criteria for Kuramoto oscillators and applies these to analyze synchronization in diverse physical systems.

Findings

Established new stability criteria using graph theory

Demonstrated synchronization in physical systems modeled as Kuramoto oscillators

Validated theoretical results through simulations

Abstract

Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one another at first glance, the true magic lies in their ability to influence and synchronize with one another, like a group of fireflies glowing in unison. The Kuramoto model was motivated by this phenomenon of collective synchronization, when a group of a large number of oscillators spontaneously lock to a common frequency, despite vast differences in their individual frequencies. Inspired by Kuramoto's groundbreaking work in the 1970s, this model captures the essence of how interconnected systems, ranging from biological networks to power grids, can achieve a state of synchronization. This work aims to study the stability and synchronization of Kuramoto oscillators, starting off with an introduction to Kuramoto Oscillators and it's broader applications. We then at a graph theoretic formulation for the same and establish various criterion for the stability, synchronization of Kuramoto Oscillators. Finally, we broadly analyze and experiment with various physical systems that tend to behave like Kuramoto oscillators followed by further simulations.