# Directed acyclic decomposition of Kuramoto equations

## TL;DR

This paper introduces a framework for decomposing Kuramoto oscillator networks into directed acyclic subnetworks, enabling a divide-and-conquer approach to analyze complex synchronization behaviors in large, heterogeneous networks.

## Contribution

It presents a novel method for decomposing Kuramoto networks into directed acyclic subnetworks, facilitating analysis of synchronization configurations.

## Key findings

- Decomposition method for Kuramoto networks into acyclic subnetworks
- Framework enables scalable analysis of large networks
- Supports divide-and-conquer approach for synchronization study

## Abstract

The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization configurations in a general non-uniform heterogeneous sparse network is an important yet difficult problem due to the complicated nonlinear interactions. In this paper, we develop a general framework for decomposing a Kuramoto network into smaller directed acyclic subnetworks that will form the foundation of a divide-and-conquer approach for studying the frequency synchronization configurations of large Kuramoto networks.