IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v12y2021i1d10.1038_s41467-021-24363-7.html
   My bibliography  Save this article

One-way dependent clusters and stability of cluster synchronization in directed networks

Author

Listed:
  • Matteo Lodi

    (DITEN, University of Genoa)

  • Francesco Sorrentino

    (University of New Mexico)

  • Marco Storace

    (DITEN, University of Genoa)

Abstract

Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks are directed, with flows of information or energy that propagate unidirectionally from given nodes to other nodes. Nevertheless, most of the work on cluster synchronization has focused on undirected networks. Here we characterize cluster synchronization in general directed networks. Our first observation is that, in directed networks, a cluster A of nodes might be one-way dependent on another cluster B: in this case, A may remain synchronized provided that B is stable, but the opposite does not hold. The main contribution of this paper is a method to transform the cluster stability problem in an irreducible form. In this way, we decompose the original problem into subproblems of the lowest dimension, which allows us to immediately detect inter-dependencies among clusters. We apply our analysis to two examples of interest, a human network of violin players executing a musical piece for which directed interactions may be either activated or deactivated by the musicians, and a multilayer neural network with directed layer-to-layer connections.

Suggested Citation

  • Matteo Lodi & Francesco Sorrentino & Marco Storace, 2021. "One-way dependent clusters and stability of cluster synchronization in directed networks," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
  • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-24363-7
    DOI: 10.1038/s41467-021-24363-7
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-021-24363-7
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1038/s41467-021-24363-7?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
    ---><---

    Citations

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


    Cited by:

    1. Atiyeh Bayani & Fahimeh Nazarimehr & Sajad Jafari & Kirill Kovalenko & Gonzalo Contreras-Aso & Karin Alfaro-Bittner & Rubén J. Sánchez-García & Stefano Boccaletti, 2024. "The transition to synchronization of networked systems," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    2. Bayani, Atiyeh & Alexander, Prasina & Azarnoush, Hamed & Rajagopal, Karthikeyan & Jafari, Sajad & Nazarimehr, Fahimeh, 2023. "Designing networks with specific synchronization transitions independent of the system’s dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

    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:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-24363-7. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    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.