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A geometrical approach to control and controllability of nonlinear dynamical networks

Author

Listed:
  • Le-Zhi Wang

    (School of Electrical, Computer and Energy Engineering, Arizona State University)

  • Ri-Qi Su

    (School of Electrical, Computer and Energy Engineering, Arizona State University)

  • Zi-Gang Huang

    (School of Electrical, Computer and Energy Engineering, Arizona State University
    Institute of Computational Physics and Complex Systems, Lanzhou University)

  • Xiao Wang

    (School of Biological and Health Systems Engineering, Arizona State University)

  • Wen-Xu Wang

    (School of Electrical, Computer and Energy Engineering, Arizona State University
    School of Systems Science, Beijing Normal University)

  • Celso Grebogi

    (Institute for Complex Systems and Mathematical Biology, King’s College, Meston Walk, University of Aberdeen)

  • Ying-Cheng Lai

    (School of Electrical, Computer and Energy Engineering, Arizona State University
    Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen
    Arizona State University)

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.

Suggested Citation

  • Le-Zhi Wang & Ri-Qi Su & Zi-Gang Huang & Xiao Wang & Wen-Xu Wang & Celso Grebogi & Ying-Cheng Lai, 2016. "A geometrical approach to control and controllability of nonlinear dynamical networks," Nature Communications, Nature, vol. 7(1), pages 1-11, September.
  • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms11323
    DOI: 10.1038/ncomms11323
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    Cited by:

    1. Aming Li & Yang-Yu Liu, 2020. "Controlling Network Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-19, February.
    2. Oscar Portoles & Manuel Blesa & Marieke van Vugt & Ming Cao & Jelmer P Borst, 2022. "Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task," PLOS Computational Biology, Public Library of Science, vol. 18(3), pages 1-20, March.
    3. Henry Cavanagh & Andreas Mosbach & Gabriel Scalliet & Rob Lind & Robert G. Endres, 2021. "Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    4. Alexander Tselykh & Vladislav Vasilev & Larisa Tselykh & Fernando A. F. Ferreira, 2022. "Influence control method on directed weighted signed graphs with deterministic causality," Annals of Operations Research, Springer, vol. 311(2), pages 1281-1305, April.
    5. Zhang, Rui & Wang, Xiaomeng & Cheng, Ming & Jia, Tao, 2019. "The evolution of network controllability in growing networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 257-266.
    6. Priyan Bhattacharya & Karthik Raman & Arun K Tangirala, 2022. "Discovering adaptation-capable biological network structures using control-theoretic approaches," PLOS Computational Biology, Public Library of Science, vol. 18(1), pages 1-28, January.
    7. Pang, Shao-Peng & Hao, Fei, 2018. "Target control of edge dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 14-26.

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