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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
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    References listed on IDEAS

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    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.

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