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Xinrui Ji1, Xiang Li1,2,3

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Chimera dynamics in higher-order networks differ based on network structure. Simplicial complexes favor higher-order interactions for synchronization, unlike hypergraphs, revealing key differences in chimera states.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Chimera states, a mix of synchronized and desynchronized behavior, are observed in coupled oscillator networks.
  • Higher-order interactions in networks are increasingly studied for their role in collective phenomena.
  • Understanding chimera dynamics in these complex network structures is an emerging research area.

Purpose of the Study:

  • To explore chimera-inspired dynamics in nonlocally coupled Kuramoto oscillators with higher-order interactions.
  • To investigate how different higher-order network representations (hypergraphs vs. simplicial complexes) influence synchronization and chimera states.
  • To develop a method for identifying chimera states in these networks.

Main Methods:

  • Analysis of Kuramoto oscillators on hypergraph and simplicial complex networks.
  • Investigation of synchronization patterns based on interaction order (pairwise vs. higher-order).
  • Basin stability analysis to understand the emergence and robustness of chimera states.

Main Results:

  • Hypergraph networks tend to synchronize via lower-order interactions.
  • Simplicial complex networks show a preference for higher-order interactions in synchronization.
  • Distinct chimera-inspired synchronization regions arise due to differences in network representations.
  • An explicit expression for identifying chimera states was introduced.
  • The emergence of chimera states is inherent in higher-order interaction networks, influenced by interaction strengths.

Conclusions:

  • The structural representation of higher-order networks significantly impacts chimera dynamics.
  • Simplicial complex networks offer a unique framework for observing chimera states driven by higher-order interactions.
  • This study provides a foundation for understanding chimera dynamics in complex, higher-order interaction systems.