Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Carlos, Brazil.
Department of Chemistry, Saint Louis University, St. Louis, MO, USA.
Nat Commun. 2022 Aug 17;13(1):4849. 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.
弱耦合振荡器网络对我们理解复杂系统产生了深远的影响。尽管这些模型最初被定义为具有成对相互作用的振荡器网络，但从数据重建模型的研究表明，具有三重和更高阶相互作用的超网络有普遍的贡献。在这里，我们表明，即使存在具有非线性的成对耦合，如果满足特定的三重频率共振条件，超网络也可以自发出现。实验中使用电化学振荡器和集成-点火神经元进行的模拟结果证明了这一点。通过发展全面的理论，我们通过识别出现和禁止的频率共振条件，揭示了涌现超网络的机制。此外，还表明单元之间的微观线性（差分）耦合导致耦合的平均场，其具有足够的非线性以促进超网络的形成。我们的发现揭示了超网络的明显丰富性，并为预测和设计它们的出现提供了一种建设性的方法。
