Irrelevance of linear controllability to nonlinear dynamical networks

Junjie Jiang, Ying Cheng Lai

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish (US)
Article number3961
JournalNature communications
Issue number1
StatePublished - Dec 1 2019

ASJC Scopus subject areas

  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology
  • General Physics and Astronomy


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