A geometrical approach to control and controllability of nonlinear dynamical networks

Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi, Ying-Cheng Lai

Research output: Contribution to journalArticle

39 Citations (Scopus)
4 Downloads (Pure)

Abstract

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Original languageEnglish
Article number11323
JournalNature Communications
Volume7
DOIs
Publication statusPublished - 14 Apr 2016

Fingerprint

Nonlinear Dynamics
Gene Regulatory Networks
controllability
Controllability
Noise
Theoretical Models
Nonlinear networks
Complex networks
Genes
perturbation
genes

Keywords

  • q-bio.MN
  • cs.SY
  • nlin.CD
  • physics.bio-ph

Cite this

A geometrical approach to control and controllability of nonlinear dynamical networks. / Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng.

In: Nature Communications, Vol. 7, 11323, 14.04.2016.

Research output: Contribution to journalArticle

Wang, Le-Zhi ; Su, Ri-Qi ; Huang, Zi-Gang ; Wang, Xiao ; Wang, Wen-Xu ; Grebogi, Celso ; Lai, Ying-Cheng. / A geometrical approach to control and controllability of nonlinear dynamical networks. In: Nature Communications. 2016 ; Vol. 7.
@article{7400069049e9456fa57efc5b3cad151d,
title = "A geometrical approach to control and controllability of nonlinear dynamical networks",
abstract = "In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.",
keywords = "q-bio.MN, cs.SY, nlin.CD, physics.bio-ph",
author = "Le-Zhi Wang and Ri-Qi Su and Zi-Gang Huang and Xiao Wang and Wen-Xu Wang and Celso Grebogi and Ying-Cheng Lai",
note = "Acknowledgements This work was supported by the ARO under Grant No. W911NF-14-1-0504. X.W. was supported by the NIH under Grant No. GM106081.",
year = "2016",
month = "4",
day = "14",
doi = "10.1038/ncomms11323",
language = "English",
volume = "7",
journal = "Nature Communications",
issn = "2041-1723",
publisher = "Nature Publishing Group",

}

TY - JOUR

T1 - A geometrical approach to control and controllability of nonlinear dynamical networks

AU - Wang, Le-Zhi

AU - Su, Ri-Qi

AU - Huang, Zi-Gang

AU - Wang, Xiao

AU - Wang, Wen-Xu

AU - Grebogi, Celso

AU - Lai, Ying-Cheng

N1 - Acknowledgements This work was supported by the ARO under Grant No. W911NF-14-1-0504. X.W. was supported by the NIH under Grant No. GM106081.

PY - 2016/4/14

Y1 - 2016/4/14

N2 - In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

AB - In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

KW - q-bio.MN

KW - cs.SY

KW - nlin.CD

KW - physics.bio-ph

U2 - 10.1038/ncomms11323

DO - 10.1038/ncomms11323

M3 - Article

VL - 7

JO - Nature Communications

JF - Nature Communications

SN - 2041-1723

M1 - 11323

ER -