Leader-follower synchronization of directed hypergraphs via pinning control

Although directionality has been fully explored in the network of pairwise interaction, few studies have been reported on the discussion of directionality in systems with higher-order interactions. Therefore, a 1-directed hypergraph dynamical model is proposed. Based on the Lyapunov stability theory, the global stability conditions for 1-directed hypergraph follower synchronization are derived by pinning control. Then, with the help of matrix theory, the selection of pinning node is given by studying the relationship between synchronization, network topology and coupling strength. Finally, a numerical simulation example is used to verify the effectiveness of this control strategy.