Emergent hypernetworks in weakly coupled oscillators

• Published in: Nature communications 2022-08, Vol.13 (1), p.4849-4849, Article 4849
• Main Authors: Nijholt, Eddie, Ocampo-Espindola, Jorge Luis, Eroglu, Deniz, Kiss, István Z., Pereira, Tiago
• Format: Article
• Language: English
• Subjects: 639/766/530/2801; 639/766/530/2803; Complex systems; Coupling; Electrochemistry; Emergence; Humanities and Social Sciences; multidisciplinary; Networks; Nonlinear systems; Nonlinearity; Oscillators; Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-022-32282-4

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. Networks with higher-order interactions are relevant to variety of real-world applications, they can be good description of data even if the system has only pairwise interactions. The authors uncover the hypernetwork emergence in coupled nonlinear oscillators and electrochemical experiments.