Influence of Coupling Strengths on Performance of Multiplex Consensus Networks

Abstract

In this paper, we examine the influence of intralayer and interlayer coupling strengths on multiplex network consensus. Via simulation study, two categories of consensus networks are considered, namely, autonomous consensus and leader-following consensus. Firstly, for autonomous consensus, it is showed that the convergence rate of multiplex network consensus will increase with respect to the coupling strengths of intralayer and interlayer, and then decrease, and eventually reach a steady state. Secondly, for the leader-following consensus, we employ nodal centrality, namely, degree, closeness and betweenness, to select leader agents. It is shown that, for small intralayer coupling strengths, leading those nodes with large centrality value of degree and closeness can improve convergence rates of consensus; for large intralayer coupling strengths, betweenness instead is more efficient. Furthermore, it is showed that a large amount of leader agents is not efficient to enhance the convergence rates of consensus, and a proposed range from 70% to 90% is optimal proportion to control a multiplex consensus network efficiently.