IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0191941.html
   My bibliography  Save this article

The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings

Author

Listed:
  • Zilin Gao
  • Yinhe Wang

Abstract

The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which are mainly caused by coupling effect of connection relationships between nodes. However, the connection relationships between nodes are also one main body of a time-varying dynamic complex network, and thus they may evolve with time and maybe show certain characteristic phenomena. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. Therefore, it is important to investigate theoretically the reasons in dynamics for the occurrence. Especially, from the angle of large-scale systems, how the dynamic behaviors of nodes (such as the individuals, neurons) contribute to the connection relationships is one of worthy research directions. In this paper, according to the structural balance theory of triad proposed by F. Heider, we mainly focus on the connection relationships body, which is regarded as one of the two subsystems (another is the nodes body), and try to find the dynamic mechanism of the structural balance with the internal state behaviors of the nodes. By using the Riccati linear matrix differential equation as the dynamic model of connection relationships subsystem, it is proved under some mathematic conditions that the connection relationships subsystem is asymptotical structural balance via the effects of the coupling roles with the internal state of nodes. Finally, the simulation example is given to show the validity of the method in this paper.

Suggested Citation

  • Zilin Gao & Yinhe Wang, 2018. "The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-14, January.
  • Handle: RePEc:plo:pone00:0191941
    DOI: 10.1371/journal.pone.0191941
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0191941
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0191941&type=printable
    Download Restriction: no

    References listed on IDEAS

    as
    1. Krzysztof Kułakowski & Przemysław Gawroński & Piotr Gronek, 2005. "The Heider Balance: A Continuous Approach," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 707-716.
    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. Sheykhali, Somaye & Darooneh, Amir Hossein & Jafari, Gholam Reza, 2020. "Partial balance in social networks with stubborn links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    2. Liu, Lizhi & Wang, Yinhe & Gao, Zilin, 2020. "Tracking control for the dynamic links of discrete-time complex dynamical network via state observer," Applied Mathematics and Computation, Elsevier, vol. 369(C).

    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. Vincent Antonio Traag & Paul Van Dooren & Patrick De Leenheer, 2013. "Dynamical Models Explaining Social Balance and Evolution of Cooperation," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-7, April.
    2. Du, Haifeng & He, Xiaochen & Wang, Jingjing & Feldman, Marcus W., 2018. "Reversing structural balance in signed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 780-792.
    3. Arabzadeh, S. & Sherafati, M. & Atyabi, F. & Jafari, G.R. & Kułakowski, K., 2021. "Lifetime of links influences the evolution towards structural balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    4. Malarz, Krzysztof & Kułakowski, Krzysztof, 2021. "Heider balance of a chain of actors as dependent on the interaction range and a thermal noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. Sajjad Salehi & Fattaneh Taghiyareh, 2020. "Stabilizing social structure via modifying local patterns," Journal of Combinatorial Optimization, Springer, vol. 39(4), pages 1079-1095, May.
    6. Pedro Cisneros-Velarde & Francesco Bullo, 2020. "Signed Network Formation Games and Clustering Balance," Dynamic Games and Applications, Springer, vol. 10(4), pages 783-797, December.

    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:pone00:0191941. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.