Synchronization induced by directed higher-order interactions

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 allows 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. There is increasing evidence that many higher-order interactions in complex systems are directed. Here, the authors provide a tensorial formalism for directed hypergraphs and investigate their synchronization properties generalizing the Master Stability Function approach.