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Deeper but smaller: Higher-order interactions increase linear stability but shrink basins.

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Higher-order interactions in network science can stabilize collective dynamics like synchrony but also make these states harder to reach. Understanding these opposing effects is crucial for nonlinear dynamics research.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Understanding higher-order interactions is key to collective dynamics in complex systems.
  • Previous research primarily used linear stability analysis, limiting insights into global state organization.

Purpose of the Study:

  • To investigate how higher-order interactions influence the global organization of states in dynamical networks.
  • To analyze the impact of hypergraph structures on Kuramoto oscillator dynamics.

Main Methods:

  • Analysis of identical Kuramoto oscillators on hypergraphs.
  • Comparison of linear stability and basin stability metrics.

Main Results:

  • Higher-order interactions improve linear stability for states like full synchrony.
  • Simultaneously, these interactions reduce basin stability, making target states more difficult to achieve.
  • Observed opposite effects on local stability versus global accessibility of dynamical states.

Conclusions:

  • Higher-order interactions present a dual role in collective dynamics, affecting both stability and reachability.
  • A comprehensive understanding requires examining both local (linear stability) and global (basin stability) perspectives.
  • Findings are crucial for designing and controlling complex networked systems.