IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v146y2021ics0960077921002411.html
   My bibliography  Save this article

D-dimensional oscillators in simplicial structures: Odd and even dimensions display different synchronization scenarios

Author

Listed:
  • Dai, X.
  • Kovalenko, K.
  • Molodyk, M.
  • Wang, Z.
  • Li, X.
  • Musatov, D.
  • Raigorodskii, A.M.
  • Alfaro-Bittner, K.
  • Cooper, G.D.
  • Bianconi, G.
  • Boccaletti, S.

Abstract

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple pairwise-relationships. Simplicial complexes are therefore the mathematical objects providing a faithful representation of such systems. We here present a complete theory of synchronization of D-dimensional oscillators obeying an extended Kuramoto model, and interacting by means of 1- and 2- simplices. Not only our theory fully describes and unveils the intimate reasons and mechanisms for what was observed so far with pairwise interactions, but it also offers predictions for a series of rich and novel behaviors in simplicial structures, which include: (a) a discontinuous de-synchronization transition at positive values of the coupling strength for all dimensions, (b) an extra discontinuous transition at zero coupling for all odd dimensions, and (c) the occurrence of partially synchronized states at D=2 (and all odd D) even for negative values of the coupling strength, a feature which is inherently prohibited with pairwise-interactions. Furthermore, our theory untangles several aspects of the emergent behavior: the system can never fully synchronize from disorder, and is characterized by an extreme multi-stability, in that the asymptotic stationary synchronized states depend always on the initial conditions. All our theoretical predictions are fully corroborated by extensive numerical simulations. Our results elucidate the dramatic and novel effects that higher-order interactions may induce in the collective dynamics of ensembles of coupled D-dimensional oscillators, and can therefore be of value and interest for the understanding of many phenomena observed in nature, like for instance the swarming and/or flocking processes unfolding in three or more dimensions.

Suggested Citation

  • Dai, X. & Kovalenko, K. & Molodyk, M. & Wang, Z. & Li, X. & Musatov, D. & Raigorodskii, A.M. & Alfaro-Bittner, K. & Cooper, G.D. & Bianconi, G. & Boccaletti, S., 2021. "D-dimensional oscillators in simplicial structures: Odd and even dimensions display different synchronization scenarios," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002411
    DOI: 10.1016/j.chaos.2021.110888
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002411
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110888?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jacopo Grilli & György Barabás & Matthew J. Michalska-Smith & Stefano Allesina, 2017. "Higher-order interactions stabilize dynamics in competitive network models," Nature, Nature, vol. 548(7666), pages 210-213, August.
    2. Kevin P. O’Keeffe & Hyunsuk Hong & Steven H. Strogatz, 2017. "Oscillators that sync and swarm," Nature Communications, Nature, vol. 8(1), pages 1-13, December.
    3. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    4. Antoine Bricard & Jean-Baptiste Caussin & Nicolas Desreumaux & Olivier Dauchot & Denis Bartolo, 2013. "Emergence of macroscopic directed motion in populations of motile colloids," Nature, Nature, vol. 503(7474), pages 95-98, November.
    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. Karimi Rahjerdi, Bahareh & Ramamoorthy, Ramesh & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Jafari, Sajad, 2022. "Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Tadić, Bosiljka & Chutani, Malayaja & Gupte, Neelima, 2022. "Multiscale fractality in partial phase synchronisation on simplicial complexes around brain hubs," Chaos, Solitons & Fractals, Elsevier, vol. 160(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. Hu, Xin & Wang, Zhishuang & Sun, Qingyi & Chen, Jiaxing & Zhao, Dawei & Xia, Chengyi, 2024. "Coupled propagation between one communicable disease and related two types of information on multiplex networks with simplicial complexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).
    2. Zhao, Dandan & Li, Runchao & Peng, Hao & Zhong, Ming & Wang, Wei, 2022. "Percolation on simplicial complexes," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    3. Gaurav Gardi & Steven Ceron & Wendong Wang & Kirstin Petersen & Metin Sitti, 2022. "Microrobot collectives with reconfigurable morphologies, behaviors, and functions," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    4. Zhang, Kebo & Hong, Xiao & Han, Yuexing & Wang, Bing, 2024. "Interplay of simplicial information propagation and epidemic spreading on multiplex metapopulation networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    5. Luca Gallo & Lucas Lacasa & Vito Latora & Federico Battiston, 2024. "Higher-order correlations reveal complex memory in temporal hypergraphs," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    6. Zhang, Renquan & Wei, Ting & Sun, Yifan & Pei, Sen, 2024. "Influence maximization based on simplicial contagion models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).
    7. Zhao, Dandan & Li, Runchao & Peng, Hao & Zhong, Ming & Wang, Wei, 2022. "Higher-order percolation in simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    8. Ma, Ning & Yu, Guang & Jin, Xin, 2024. "Dynamics of competing public sentiment contagion in social networks incorporating higher-order interactions during the dissemination of public opinion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Martina Contisciani & Federico Battiston & Caterina De Bacco, 2022. "Inference of hyperedges and overlapping communities in hypergraphs," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    10. Peng, Hao & Zhao, Yifan & Zhao, Dandan & Zhong, Ming & Hu, Zhaolong & Han, Jianming & Li, Runchao & Wang, Wei, 2023. "Robustness of higher-order interdependent networks," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    11. Zhang, Ziyu & Mei, Xuehui & Jiang, Haijun & Luo, Xupeng & Xia, Yang, 2023. "Dynamical analysis of Hyper-SIR rumor spreading model," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    12. Federico Malizia & Alessandra Corso & Lucia Valentina Gambuzza & Giovanni Russo & Vito Latora & Mattia Frasca, 2024. "Reconstructing higher-order interactions in coupled dynamical systems," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    13. Li, Zhaoqing & Deng, Zhenghong & Han, Zhen & Alfaro-Bittner, Karin & Barzel, Baruch & Boccaletti, Stefano, 2021. "Contagion in simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Yuanzhao Zhang & Maxime Lucas & Federico Battiston, 2023. "Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    15. Maxime Hubert & Stéphane Perrard & Nicolas Vandewalle & Matthieu Labousse, 2022. "Overload wave-memory induces amnesia of a self-propelled particle," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    16. Gong, Chang & Li, Jichao & Qian, Liwei & Li, Siwei & Yang, Zhiwei & Yang, Kewei, 2024. "HMSL: Source localization based on higher-order Markov propagation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    17. Daniel Reisinger & Fabian Tschofenig & Raven Adam & Marie Lisa Kogler & Manfred Füllsack & Fabian Veider & Georg Jäger, 2024. "Patterns of stability in complex contagions," Journal of Computational Social Science, Springer, vol. 7(2), pages 1895-1911, October.
    18. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    19. Guilherme Ferraz de Arruda & Giovanni Petri & Pablo Martin Rodriguez & Yamir Moreno, 2023. "Multistability, intermittency, and hybrid transitions in social contagion models on hypergraphs," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    20. Nie, Yanyi & Li, Wenyao & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Markovian approach to tackle competing pathogens in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 417(C).

    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:eee:chsofr:v:146:y:2021:i:c:s0960077921002411. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.