Irrelevance of linear controllability to nonlinear dynamical networks

Junjie Jiang and Ying-Cheng Lai ()
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Junjie Jiang: Arizona State University
Ying-Cheng Lai: Arizona State University

Nature Communications, 2019, vol. 10, issue 1, 1-10

Abstract: Abstract There has been tremendous development in 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 the irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to Caenorhabditis elegans connectome is examined and discussed.

Date: 2019
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DOI: 10.1038/s41467-019-11822-5

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