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Cluster synchronization and isolated desynchronization in complex networks with symmetries

Author

Listed:
  • Louis M. Pecora

    (US Naval Research Laboratory)

  • Francesco Sorrentino

    (University of New Mexico)

  • Aaron M. Hagerstrom

    (University of Maryland
    Institute for Research in Electronics and Applied Physics, University of Maryland)

  • Thomas E. Murphy

    (Institute for Research in Electronics and Applied Physics, University of Maryland
    University of Maryland)

  • Rajarshi Roy

    (Institute for Research in Electronics and Applied Physics, University of Maryland
    University of Maryland
    Institute for Physical Science and Technology, University of Maryland)

Abstract

Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the analysis of network dynamics that shows the connection between network symmetries and cluster formation. The connection between symmetries and cluster synchronization is experimentally confirmed in the context of real networks with heterogeneities and noise using an electro-optic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony without disturbing the others. Our analysis shows that such behaviour will occur in a wide variety of networks and node dynamics. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behaviour of networks ranging from neural to social.

Suggested Citation

  • Louis M. Pecora & Francesco Sorrentino & Aaron M. Hagerstrom & Thomas E. Murphy & Rajarshi Roy, 2014. "Cluster synchronization and isolated desynchronization in complex networks with symmetries," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    • Handle: RePEc:nat:natcom:v:5:y:2014:i:1:d:10.1038_ncomms5079
    DOI: 10.1038/ncomms5079
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    3. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Rybalova, E.V. & Zakharova, A. & Strelkova, G.I., 2021. "Interplay between solitary states and chimeras in multiplex neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. Vieira, Robson & Martins, Weliton S. & Barreiro, Sergio & Oliveira, Rafael A. de & Chevrollier, Martine & Oriá, Marcos, 2021. "Synchronization of a nonlinear oscillator with a sum signal from equivalent oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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    7. Minati, Ludovico & Innocenti, Giacomo & Mijatovic, Gorana & Ito, Hiroyuki & Frasca, Mattia, 2022. "Mechanisms of chaos generation in an atypical single-transistor oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. Huang, Changwei & Luo, Yijun & Han, Wenchen, 2023. "Cooperation and synchronization in evolutionary opinion changing rate games," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    9. Chai, Yuan & Xu, Li & Zhang, Hudong, 2021. "Interchangeable outer synchronization of community networks with two spatiotemporal clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    10. Minati, Ludovico & Li, Chao & Bartels, Jim & Chakraborty, Parthojit & Li, Zixuan & Yoshimura, Natsue & Frasca, Mattia & Ito, Hiroyuki, 2023. "Accelerometer time series augmentation through externally driving a non-linear dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. Shepelev, I.A. & Bukh, A.V. & Strelkova, G.I., 2022. "Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    12. Ye, Jiachen & Ji, Peng & Waxman, David & Lin, Wei & Moreno, Yamir, 2020. "Impact of intra and inter-cluster coupling balance on the performance of nonlinear networked systems," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Minati, Ludovico & Bartels, Jim & Li, Chao & Frasca, Mattia & Ito, Hiroyuki, 2022. "Synchronization phenomena in dual-transistor spiking oscillators realized experimentally towards physical reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Tommaso Menara & Giacomo Baggio & Dani Bassett & Fabio Pasqualetti, 2022. "Functional control of oscillator networks," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    15. Shepelev, I.A. & Vadivasova, T.E., 2021. "Synchronization in multiplex networks of chaotic oscillators with frequency mismatch," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    16. Muolo, Riccardo & Carletti, Timoteo & Bianconi, Ginestra, 2024. "The three way Dirac operator and dynamical Turing and Dirac induced patterns on nodes and links," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    17. Wu, Xifen & Bao, Haibo, 2020. "Finite time complete synchronization for fractional-order multiplex networks," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    18. Khanra, Pitambar & Ghosh, Subrata & Alfaro-Bittner, Karin & Kundu, Prosenjit & Boccaletti, Stefano & Hens, Chittaranjan & Pal, Pinaki, 2022. "Identifying symmetries and predicting cluster synchronization in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    19. Minati, Ludovico & Li, Boyan & Bartels, Jim & Li, Zixuan & Frasca, Mattia & Ito, Hiroyuki, 2022. "Incomplete synchronization of chaos under frequency-limited coupling: Observations in single-transistor microwave oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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