Explosive higher-order Kuramoto dynamics on simplicial complexes

TL;DR

This paper introduces a higher-order Kuramoto model on simplicial complexes that captures interactions across nodes and higher-dimensional simplices, revealing an explosive synchronization transition influenced by adaptive coupling.

Contribution

It extends traditional Kuramoto models to include higher-order interactions on simplicial complexes, demonstrating explosive synchronization phenomena.

Findings

Higher-order interactions induce explosive synchronization.

Adaptive coupling based on solenoidal and irrotational components drives the transition.

Model captures complex system dynamics like those in the brain.

Abstract

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.