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

Author

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  • 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
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    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).

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