# Irrelevance of linear controllability to nonlinear dynamical networks

arXiv: https://arxiv.org/abs/1909.01288 · HTML: https://mlsanity.com/paper/1909.01288/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Federated Nonlinear System Identification](https://mlsanity.com/paper/2508.15025/) (2025)

## Abstract (arXiv)

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