Irrelevance of linear controllability to nonlinear dynamical networks

Area of Science:

• Complex networks
• Control theory
• Systems biology

Background:

• Complex networks are ubiquitous in nature and technology.
• Linear controllability has been extensively studied for network control.
• Real-world systems are fundamentally nonlinear, questioning the applicability of linear control.

Purpose of the Study:

• To investigate the relevance of linear controllability to nonlinear dynamical networks.
• To identify commonalities and differences in nodal importance for linear and nonlinear control.
• To evaluate the applicability of linear control theory to empirical biological networks.

Main Methods:

• Analysis of nodal importance in empirical mutualistic networks and a gene regulatory network.
• Quantification of nonlinear nodal importance using system restoration after tipping-point transitions.
• Comparison of nodal importance rankings between linear and nonlinear control frameworks.

Main Results:

• Nodal importance rankings for linear and nonlinear control exhibit opposite trends.
• Large-degree nodes are more critical for nonlinear control, while small-degree nodes are prioritized in linear control.
• Evidence suggests linear controllability is largely irrelevant for the studied nonlinear systems.

Conclusions:

• Linear controllability may not be a reliable indicator of control importance in nonlinear complex networks.
• Nodal importance is context-dependent, differing significantly between linear and nonlinear dynamics.
• The application of linear controllability to biological connectomes like C. elegans requires careful re-examination.