IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v13y2022i1d10.1038_s41467-022-32282-4.html
   My bibliography  Save this article

Emergent hypernetworks in weakly coupled oscillators

Author

Listed:
  • Eddie Nijholt

    (Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo)

  • Jorge Luis Ocampo-Espindola

    (Saint Louis University)

  • Deniz Eroglu

    (Kadir Has University)

  • István Z. Kiss

    (Saint Louis University)

  • Tiago Pereira

    (Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo
    Department of Mathematics, Imperial College London)

Abstract

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.

Suggested Citation

  • Eddie Nijholt & Jorge Luis Ocampo-Espindola & Deniz Eroglu & István Z. Kiss & Tiago Pereira, 2022. "Emergent hypernetworks in weakly coupled oscillators," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32282-4
    DOI: 10.1038/s41467-022-32282-4
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-022-32282-4
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/s41467-022-32282-4?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
    ---><---

    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. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    3. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
    4. Björn Kralemann & Matthias Frühwirth & Arkady Pikovsky & Michael Rosenblum & Thomas Kenner & Jochen Schaefer & Maximilian Moser, 2013. "In vivo cardiac phase response curve elucidates human respiratory heart rate variability," Nature Communications, Nature, vol. 4(1), pages 1-9, December.
    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. 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.

    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. Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.
    2. Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.
    3. Mark L Ioffe & Michael J Berry II, 2017. "The structured ‘low temperature’ phase of the retinal population code," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    4. Chen, Hsien-Keng, 2005. "Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1049-1056.
    5. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Hoang, Thang Manh, 2011. "Complex synchronization manifold in coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 48-57.
    7. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.
    8. Maulana, Ardian & Situngkir, Hokky, 2015. "Korelasi Bebas-skala dalam Studi Geo-politik Pemilihan [Scale-free correlation within Geopolitics of Election Studies]," MPRA Paper 66351, University Library of Munich, Germany.
    9. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.
    10. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Hideaki Shimazaki & Shun-ichi Amari & Emery N Brown & Sonja Grün, 2012. "State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-27, March.
    12. Timothy R Lezon & Ivet Bahar, 2010. "Using Entropy Maximization to Understand the Determinants of Structural Dynamics beyond Native Contact Topology," PLOS Computational Biology, Public Library of Science, vol. 6(6), pages 1-12, June.
    13. Sacha Jennifer van Albada & Moritz Helias & Markus Diesmann, 2015. "Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-37, September.
    14. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
    15. Sahar Gelfman & Quanli Wang & Yi-Fan Lu & Diana Hall & Christopher D Bostick & Ryan Dhindsa & Matt Halvorsen & K Melodi McSweeney & Ellese Cotterill & Tom Edinburgh & Michael A Beaumont & Wayne N Fran, 2018. "meaRtools: An R package for the analysis of neuronal networks recorded on microelectrode arrays," PLOS Computational Biology, Public Library of Science, vol. 14(10), pages 1-20, October.
    16. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    17. Jason S Prentice & Olivier Marre & Mark L Ioffe & Adrianna R Loback & Gašper Tkačik & Michael J Berry II, 2016. "Error-Robust Modes of the Retinal Population Code," PLOS Computational Biology, Public Library of Science, vol. 12(11), pages 1-32, November.
    18. Alicia Sanchez-Gorostiaga & Djordje Bajić & Melisa L Osborne & Juan F Poyatos & Alvaro Sanchez, 2019. "High-order interactions distort the functional landscape of microbial consortia," PLOS Biology, Public Library of Science, vol. 17(12), pages 1-34, December.
    19. Martin-I. Trappe & Ryan A. Chisholm, 2023. "A density functional theory for ecology across scales," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    20. Montani, Fernando & Phoka, Elena & Portesi, Mariela & Schultz, Simon R., 2013. "Statistical modelling of higher-order correlations in pools of neural activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3066-3086.

    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:13:y:2022:i:1:d:10.1038_s41467-022-32282-4. 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: 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.