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Emergent hypernetworks in weakly coupled oscillators.

Eddie Nijholt1, Jorge Luis Ocampo-Espindola2, Deniz Eroglu3

  • 1Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Carlos, Brazil.

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Summary
This summary is machine-generated.

Hypernetworks with higher-order interactions can emerge in oscillator networks with only pairwise coupling under specific frequency resonance conditions. This finding explains the prevalence of hypernetworks and offers methods for their prediction and engineering.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Networks of weakly coupled oscillators are crucial for understanding complex systems.
  • Previous studies identified hypernetworks with higher-order interactions, despite models initially focusing on pairwise interactions.

Purpose of the Study:

  • To demonstrate the spontaneous emergence of hypernetworks from pairwise coupled oscillator systems.
  • To uncover the underlying mechanism and conditions for emergent hypernetworks.

Main Methods:

  • Theoretical analysis of emergent hypernetworks.
  • Experimental validation using electrochemical oscillators.
  • Simulations with integrate-and-fire neurons.

Main Results:

  • Hypernetworks spontaneously emerge in pairwise coupled oscillator networks under specific triplet frequency resonance conditions.
  • A comprehensive theory identified emergent and forbidden frequency resonant conditions.
  • Microscopic linear coupling leads to nonlinear coupled mean fields that facilitate hypernetworks.

Conclusions:

  • Explains the prevalence of hypernetworks in complex systems.
  • Provides a framework for predicting and engineering hypernetwork emergence.
  • Highlights the role of nonlinear dynamics in pairwise coupled systems.