On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks

This paper presents some low-dimensional pinning criteria for global synchronization of both directed and undirected complex networks, and proposes specifically pinning schemes to select pinned nodes by investigating the relationship among pinning synchronization, network topology, and the coupling strength. The paper answers the challenging questions in pinning control of complex networks: 1) what sufficient conditions can guarantee global asymptotic stability of the pinning process; 2) what nodes should be chosen as pinned candidates; and 3) how many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed to achieve synchronization of general complex networks. Numerical examples are given to verify our theoretical analysis.