Regulating synchronous states of complex networks by pinning interaction with an external node

Abstract

An initial ensemble of networking dynamical systems is regulated towards a desired synchronized behavior by means of a pinning interaction with an external node. We rigorously demonstrate that there are two classes of networks susceptible of being regulated into a synchronous motion, and practically demonstrate, for each one of them, how to design a proper minimal, optimal, and maximal pinning sequence to achieve synchrony regulation. A series of numerical examples are offered to support our analytical claims. We also discuss how the obtained sequences can be compared with a topological ranking of the network nodes, such as centrality, and the practical applications of our study in the understanding of how networking systems can adjust their architecture in order to establish (or maintain) a synchronous functioning.