TY - JOUR
T1 - Irrelevance of linear controllability to nonlinear dynamical networks
AU - Jiang, Junjie
AU - Lai, Ying Cheng
N1 - Publisher Copyright:
© 2019, The Author(s).
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85071758061&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85071758061&partnerID=8YFLogxK
U2 - 10.1038/s41467-019-11822-5
DO - 10.1038/s41467-019-11822-5
M3 - Article
C2 - 31481693
AN - SCOPUS:85071758061
SN - 2041-1723
VL - 10
JO - Nature communications
JF - Nature communications
IS - 1
M1 - 3961
ER -