A double explosive Kuramoto transition in hypergraphs

TL;DR

This paper investigates how higher-order interactions and partial adaptation in hypergraphs can induce double explosive phase transitions in synchronization, expanding understanding of complex network dynamics.

Contribution

It introduces the concept of double explosive transitions in hypergraphs driven by triadic interactions and partial adaptation, supported by analytical and numerical methods.

Findings

Double explosive transitions can occur in hypergraphs with triadic interactions.

Partial adaptation of the global order parameter influences transition nature.

Numerical simulations confirm the theoretical predictions.

Abstract

This study aims to develop a generalised concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. To reinforce numerical observations, we employed the Ott--Antonsen ansatz. We observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition.