Performance of leader-following consensus on multiplex networks

A multiplex network is derived from the interplay between the intralayer and interlayer networks. This paper examines the performance of controlling consensus dynamics on multiplex networks via leader-following approach. Regardless of the topological location of leaders and the topology of intralayer networks, it is shown that the proportion of leaders plays a central role in the convergence rate of leader-following consensus on multiplex networks, especially for large networks. We show that the convergence rate of leader-following multiplex consensus is monotonically increasing with respect to the proportion of leaders and its upper bound is invariant to the topology of the intralayer network. It turns out that the Erdős-Rényi random multiplex networks are easier to control compared with scale-free multiplex networks in terms of convergence rate of leader-following consensus. The polynomial regression analysis is also employed to fit the correlation between the proportion of leaders and the convergence rate of leader-following consensus on multiplex networks. Our findings shed light on the understanding of propagation of either friendly or malicious influence exerted on a multiplex network.