Controllability of multiplex, multi-timescale networks

Abstract

The paradigm of layered networks is used to describe many real-world systems -- from biological networks, to social organizations and transportation systems. Recently there has been much progress in understanding the general properties of multilayer networks, our understanding of how to control such systems remains limited. One aspect that makes this endeavor challenging is that each layer can operate at a different timescale, thus we cannot directly apply standard ideas from structural control theory of individual networks. Here we address the problem of controlling multilayer and multi-timescale networks focusing on two-layer multiplex networks with one-to-one interlayer coupling. We investigate the case when the control signal is applied to the nodes of one layer. We develop a theory based on disjoint path covers to determine the minimum number of inputs ($N_\T i$) necessary for full control. We show that if both layers operate on the same timescale then the network structure of both layers equally affect controllability. In the presence of timescale separation, controllability is enhanced if the controller interacts with the faster layer: $N_\T i$ decreases as the timescale difference increases up to a critical timescale difference, above which $N_\T i$ remains constant and is completely determined by the faster layer. In contrast, control becomes increasingly difficult if the controller interacts with the layer operating on the slower timescale and increasing timescale separation leads to increased $N_\T i$, again up to a critical value, above which $N_\T i$ still depends on the structure of both layers. By identifying the underlying mechanisms that connect timescale difference and controllability for a simplified model, we provide insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity.

References in corpus (22)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Catastrophic cascade of failures in interdependent networks
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Diffusion dynamics on multiplex networks
• Exact Controllability of Complex Networks
• Suppressing cascades of load in interdependent networks
• Pinning-controllability of complex networks
• Realistic Control of Network Dynamics
• Emergence of bimodality in controlling complex networks
• Percolation in Directed Scale-Free Networks
• Effect of correlations on network controllability
• The number of matchings in random graphs
• Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks
• Core percolation on complex networks
• Core percolation in random graphs: a critical phenomena analysis
• Critical random graphs: Diameter and mixing time
• Control of Multilayer Networks
• Value of peripheral nodes in controlling multilayer networks
• Core percolation and onset of complexity in Boolean networks

Cited by in corpus (12)

• Collective phenomena emerging from the interactions between dynamical processes in multiplex networks
• Optimal percolation on multiplex networks
• Perspectives on adaptive dynamical systems
• Multilayer Network Science: from Cells to Societies
• Energy cost study for controlling complex social networks with conformity behavior
• Diversity of structural controllability of complex networks with given degree sequence
• The evolution of network controllability in growing networks
• The network asymmetry caused by the degree correlation and its effect on the bimodality in control
• Observability transition in multiplex networks
• Heuristic assessment of the economic effects of pandemic control
• Deep Learning Super-Diffusion in Multiplex Networks
• Controllability analysis of directed networks in finite states based on pruning motif isomorph