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Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes.

Ana P Millán1, Joaquín J Torres2, Ginestra Bianconi3

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Summary
This summary is machine-generated.

This study introduces a new higher-order Kuramoto model for complex systems, revealing how interactions beyond nodes drive explosive synchronization transitions in network dynamics.

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Area of Science:

  • Complex systems science
  • Network dynamics
  • Mathematical physics

Background:

  • Complex systems exhibit higher-order interactions, crucial for their dynamics, often represented by simplicial complexes.
  • Existing dynamical models on simplicial complexes typically assume dynamics are confined to nodes, neglecting higher-order structures.

Purpose of the Study:

  • To formulate a novel higher-order Kuramoto model incorporating dynamics on nodes, links, and higher-dimensional simplices.
  • To investigate the synchronization transitions in complex systems using this enhanced model.

Main Methods:

  • Development of the higher-order Kuramoto model accounting for interactions across all simplicial complex elements.
  • Utilizing adaptive coupling mechanisms dependent on the solenoidal and irrotational components of the dynamics.

Main Results:

  • The higher-order Kuramoto model demonstrates the capability to induce explosive synchronization transitions.
  • Adaptive coupling based on solenoidal and irrotational dynamics significantly influences synchronization behavior.

Conclusions:

  • Higher-order interactions are essential for understanding synchronization phenomena in complex systems.
  • The proposed model offers a more comprehensive framework for studying network dynamics and emergent behaviors like explosive synchronization.