Emergent hypernetworks in weakly coupled oscillators

TL;DR

This paper demonstrates that hypernetworks with higher-order interactions can spontaneously emerge in systems of weakly coupled oscillators due to specific frequency resonance conditions, supported by experiments and theory.

Contribution

It reveals the mechanism behind emergent hypernetworks in pairwise coupled oscillators through resonance conditions and develops a comprehensive theory for their prediction and control.

Findings

Hypernetworks can spontaneously form under certain triplet frequency resonances.

Linear coupling among oscillators leads to nonlinear mean fields that facilitate hypernetworks.

The theory predicts conditions for hypernetwork emergence in experimental and simulated systems.

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.