IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0038398.html
   My bibliography  Save this article

Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks

Author

Listed:
  • Noah J Cowan
  • Erick J Chastain
  • Daril A Vilhena
  • James S Freudenberg
  • Carl T Bergstrom

Abstract

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167–173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

Suggested Citation

  • Noah J Cowan & Erick J Chastain & Daril A Vilhena & James S Freudenberg & Carl T Bergstrom, 2012. "Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-5, June.
    • Handle: RePEc:plo:pone00:0038398
    DOI: 10.1371/journal.pone.0038398
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0038398
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0038398&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0038398?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Xiang, L.Y. & Liu, Z.X. & Chen, Z.Q. & Chen, F. & Yuan, Z.Z., 2007. "Pinning control of complex dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 298-306.
    2. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    3. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    4. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    5. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mariolis, Theodore, 2019. "The location of the value theories in the complex plane and the degree of regularity-controllability of actual economies," MPRA Paper 96972, University Library of Munich, Germany.
    2. Wang, Jiqiang, 2019. "Disturbance attenuation of complex dynamical systems through interaction topology design," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 576-584.
    3. Rabajante, Jomar Fajardo & Talaue, Cherryl Ortega, 2015. "Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 166-182.
    4. Han, Fangyuan & Zio, Enrico, 2019. "A multi-perspective framework of analysis of critical infrastructures with respect to supply service, controllability and topology," International Journal of Critical Infrastructure Protection, Elsevier, vol. 24(C), pages 1-13.
    5. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Berryhill, Benjamin & Yazdani, Alireza, 2016. "Characterizing the topological and controllability features of U.S. power transmission networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 84-98.
    6. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    7. David L Gibbs & Ilya Shmulevich, 2017. "Solving the influence maximization problem reveals regulatory organization of the yeast cell cycle," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-19, June.
    8. Yin, Hongli & Zhang, Siying, 2016. "Minimum structural controllability problems of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 467-476.
    9. Nie, Sen & Wang, Xuwen & Wang, Binghong, 2015. "Effect of degree correlation on exact controllability of multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 98-102.
    10. e Sousa, Álan & Messai, Nadhir & Manamanni, Noureddine, 2022. "Load-altering attack detection on smart grid using functional observers," International Journal of Critical Infrastructure Protection, Elsevier, vol. 37(C).
    11. Theodore Mariolis & Despoina Kesperi, 2022. "Demand multipliers and technical performance of a Southern Eurozone economy in hard times: Kalman–Leontief–Sraffa evidence from the Greek economy, 2010–2014," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 47-75, April.
    12. Guilherme Ramos & Sérgio Pequito, 2020. "Generating complex networks with time-to-control communities," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-12, August.
    13. Chen, Shi-Ming & Xu, Yun-Fei & Nie, Sen, 2017. "Robustness of network controllability in cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 536-539.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    2. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    3. Luo, Mengzhuo & Liu, Xinzhi & Zhong, Shouming & Cheng, Jun, 2018. "Synchronization of stochastic complex networks with discrete-time and distributed coupling delayed via hybrid nonlinear and impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 381-393.
    4. Li, Xin-Feng & Lu, Zhe-Ming, 2016. "Optimizing the controllability of arbitrary networks with genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 422-433.
    5. Wang, Jiqiang, 2019. "Disturbance attenuation of complex dynamical systems through interaction topology design," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 576-584.
    6. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    7. Liu, Tao & Dimirovski, Georgi M. & Zhao, Jun, 2008. "Exponential synchronization of complex delayed dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 643-652.
    8. Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    9. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    10. T. Botmart & N. Yotha & P. Niamsup & W. Weera, 2017. "Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings," Complexity, Hindawi, vol. 2017, pages 1-18, August.
    11. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    12. Miao, Qingying & Rong, Zhihai & Tang, Yang & Fang, Jianan, 2008. "Effects of degree correlation on the controllability of networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6225-6230.
    13. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    14. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    15. L. Jarina Banu & P. Balasubramaniam, 2014. "Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1427-1450, July.
    16. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    17. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    18. Christos Ellinas & Neil Allan & Anders Johansson, 2016. "Exploring Structural Patterns Across Evolved and Designed Systems: A Network Perspective," Systems Engineering, John Wiley & Sons, vol. 19(3), pages 179-192, May.
    19. Hiroyasu Inoue, 2015. "Analyses of Aggregate Fluctuations of Firm Network Based on the Self-Organized Criticality Model," Papers 1512.05066, arXiv.org, revised Apr 2016.
    20. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0038398. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.