Controllability of higher-order networks

Higher-order networks can comprehensively describe interactions among groups, thus emerging as a novel area of exploration in network science. This paper aims to delve into the controllability of higher-order networks, where the network topology is characterized by higher-order interactions and the nodes are higher-dimensional dynamical systems. The collective effects on the network controllability from the dynamics of higher-order interactions, node dynamics, inner interactions, and external control inputs are extensively explored. By applying matrix theory and control theory, some necessary and/or sufficient conditions are developed to determine the controllability of hypergraph networks and simplicial complex networks. Through simulated examples, it becomes evident that the controllability of higher-order networked system is far more complicated than that of traditional networked systems and the higher-order topological structures facilitate the controllability. Remarkably, the integrated network can achieve controllability even when the corresponding traditional network is uncontrollable by external inputs. •The network topology is general and characterized by higher-order interactions.•Some criteria for the controllability of the higher-order networks are developed.•The controllability between higher-order networks and complex networks are compared.•The controllability is influenced by the node dynamics and higher-order interactions.