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.

L. Gallo, R. Muolo, L. V. Gambuzza, V. Latora, M. Frasca, T. Carletti, Synchronization induced by directed higher-order interactions, Communications Physics 5 (2022) 263