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Emergence and Control of Synchronization in Networks with Directed Many-Body Interactions.

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Summary
This summary is machine-generated.

Higher-order interactions on hypergraphs drive synchronization in dynamical systems. This study introduces a diffusion mechanism, analogous to signed graphs, explaining collective behavior onset and mathematically verifying convergence to synchronous states.

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Area of Science:

  • Complex systems
  • Network science
  • Dynamical systems theory

Background:

  • Collective behaviors in dynamical networks are often attributed to pairwise interactions and diffusive coupling.
  • Understanding the impact of higher-order interactions on synchronization remains a key challenge.

Purpose of the Study:

  • To investigate how higher-order interactions influence the onset of spontaneous or induced synchronization in networks.
  • To propose and analyze a novel diffusion mechanism over hypergraphs for synchronization.

Main Methods:

  • Development of a diffusion mechanism model on hypergraphs.
  • Utilizing an analogy with signed graphs to clarify the synchronization process.
  • Mathematical analysis to derive general conditions for convergence to the synchronous state.

Main Results:

  • The proposed hypergraph diffusion mechanism effectively explains the onset of synchronization.
  • The analogy with signed graphs provides a clear framework for understanding the role of higher-order interactions.
  • General mathematical conditions for achieving synchronization were established.

Conclusions:

  • Higher-order interactions, modeled via hypergraphs, play a crucial role in network synchronization.
  • The developed diffusion mechanism offers a new perspective on collective behavior in complex systems.
  • The findings provide a theoretical foundation for controlling synchronization in engineered and physical systems.