Emergence and control of synchronization in networks with directed many-body interactions

TL;DR

This paper investigates how higher-order interactions in directed hypergraph networks influence the emergence and control of synchronization, providing mathematical conditions for achieving collective synchronous behavior.

Contribution

It introduces a diffusion mechanism over hypergraphs to explain synchronization, extending traditional pairwise interaction models with a novel higher-order interaction framework.

Findings

Derived general conditions for convergence to synchronization

Established an analogy with signed graphs for understanding synchronization

Demonstrated the impact of higher-order interactions on collective behavior

Abstract

The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or induced synchronous behavior? Inspired by actuation and measurement constraints typical of physical and engineered systems, we propose a diffusion mechanism over hypergraphs that explains the onset of synchronization through a clarifying analogy with signed graphs. Our findings are mathematically backed by general conditions for convergence to the synchronous state.