Leader-Follower Synchronization of High-Dimensional Networks Over Finite Fields

This paper investigates the synchronization problem of high-dimensional leader-follower networks over finite fields. By analyzing the transition graph of finite field networks, the relationship between the cycle spaces of the studied networks and the leader-subnetwork is revealed. Based on characteristic polynomials and ranks of matrices, several equivalent conditions for the leader-follower synchronization and leader-follower consensus of networks over finite fields are derived, respectively. In addition, an algebraic formula for calculating the cycle space of finite field networks is proposed. Finally, a specific structure model and some numerical examples are presented to validate the obtained theoretical results.