Irrelevance of linear controllability to nonlinear dynamical networks

Abstract

There has been tremendous development of linear controllability of complex networks. Real-world systems are fundamentally nonlinear. Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal "importance." For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to C. elegans connectome is examined and discussed.

arXiv comment26 pages, 8 figures

References in corpus (16)

• Controllability of Brain Networks
• Control Principles of Complex Networks
• Exact Controllability of Complex Networks
• On Submodularity and Controllability in Complex Dynamical Networks
• Pinning-controllability of complex networks
• Controlling edge dynamics in complex networks
• Controlling complex networks: How much energy is needed?
• Structure-based control of complex networks with nonlinear dynamics
• Developmental increases in white matter network controllability support a growing diversity of brain dynamics
• Control of Dynamics in Brain Networks
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• The number of matchings in random graphs
• Energy Scaling of Targeted Optimal Control of Complex Networks
• Locally Optimal Control of Complex Networks
• Structurally Robust Control of Complex Networks
• Introduction to the Special Issue on Approaches to Control Biological and Biologically Inspired Networks

Cited by in corpus (5)

• Network resilience
• Model-free tracking control of complex dynamical trajectories with machine learning
• The control of brain network dynamics across diverse scales of space and time
• Energy cost study for controlling complex social networks with conformity behavior
• Controlling Complex Systems