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Title: Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics
Authors: Kashima, Kenji  kyouindb  KAKEN_id  orcid (unconfirmed)
Author's alias: 加嶋, 健司
Issue Date: 6-Jun-2016
Publisher: Nature Publishing Group
Journal title: Scientific Reports
Volume: 6
Thesis number: 27300
Abstract: Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics.
Rights: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit
DOI(Published Version): 10.1038/srep27300
PubMed ID: 27264780
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