Heterogeneity of Central Nodes Explains the Benefits of Time-Varying Control in Complex Dynamical Networks

TL;DR

This paper demonstrates that time-varying control schedules can significantly improve the controllability of complex networks, especially when central nodes vary across different spatial scales, highlighting the importance of network heterogeneity.

Contribution

It introduces a scale-dependent centrality framework to explain when and why time-varying control outperforms traditional fixed schedules in complex networks.

Findings

TVCS enhances controllability over TICS, especially in large networks.

Optimal TVCS involves actuating the most central nodes at appropriate scales.

Network heterogeneity in central nodes determines TVCS effectiveness.

Abstract

Despite extensive research and remarkable advancements in the control of complex dynamical networks, most studies and practical control methods limit their focus to time-invariant control schedules (TICS). This is both due to their simplicity and the fact that the benefits of time-varying control schedules (TVCS) have remained largely uncharacterized. In this paper we study networks with linear and discrete-time dynamics and analyze the role of network structure in TVCS. First, we show that TVCS can significantly enhance network controllability over TICS, especially when applied to large networks. Through the analysis of a scale-dependent notion of nodal centrality, we then show that optimal TVCS involves the actuation of the most central nodes at appropriate spatial scales at all times. Consequently, it is the scale-heterogeneity of the central-nodes in a network that determine whether, and to what extent, TVCS outperforms conventional policies based on TICS. Here, scale-heterogeneity of a network refers to how diverse the central nodes of the network are at different spatial (local vs. global) scales. Several analytical results and case studies support and illustrate this relationship.