Irrelevance of linear controllability to nonlinear dynamical networks

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...

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Bibliographic Details
Published in:Nature communications 2019-09, Vol.10 (1), p.3961-10, Article 3961
Main Authors: Jiang, Junjie, Lai, Ying-Cheng
Format: Article
Language:English
Subjects:
631/158
631/553/2702
639/766/530/2801
639/766/530/2803
Algorithms
Animals
Caenorhabditis elegans - genetics
Computer Simulation
Controllability
Dynamical systems
Gene Regulatory Networks
Humanities and Social Sciences
Linear control
Magnoliopsida - genetics
Models, Biological
multidisciplinary
Nematodes
Networks
Nodes
Nonlinear control
Nonlinear Dynamics
Nonlinear systems
Pollination
Saccharomyces cerevisiae - genetics
Science
Science (multidisciplinary)
Stability
Symbiosis
Transcription, Genetic
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Summary: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. Linear controllability theories have stimulated research on control of complex networks. Here the authors investigate the concordance between linear and nonlinear approaches in ranking the importance of nodes in nonlinear networks, and conclude that linear controllability may not be applicable.
ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-019-11822-5