# Explosive higher-order Kuramoto dynamics on simplicial complexes

arXiv: https://arxiv.org/abs/1912.04405 · HTML: https://mlsanity.com/paper/1912.04405/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 5 of 5)

- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Explosive neural networks via higher-order interactions in curved statistical manifolds](https://mlsanity.com/paper/2408.02326/) (2024)
- [Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning](https://mlsanity.com/paper/2412.05132/) (2024)

## Abstract (arXiv)

The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.