Synchronization induced by directed higher-order interactions

TL;DR

This paper introduces M-directed hypergraphs to study how directed higher-order interactions influence synchronization in complex systems, revealing they can both disrupt and stabilize synchronized states.

Contribution

The paper pioneers the analysis of directed higher-order interactions using M-directed hypergraphs and explores their impact on oscillator synchronization.

Findings

Directed higher-order interactions can destroy synchronization.

They can also stabilize otherwise unstable synchronized states.

The framework advances understanding of non-reciprocal interactions in complex systems.

Abstract

Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order interactions have not yet been explored as deserved. Here, we introduce the concept of M-directed hypergraphs, a general class of directed higher-order structures, which allow to investigate dynamical systems coupled through directed group interactions. As an application we study the synchronization of nonlinear oscillators on 1-directed hypergraphs, finding that directed higher-order interactions can destroy synchronization, but also stabilize otherwise unstable synchronized states.