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Multiple first-order transitions in simplicial complexes on multilayer systems.

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Higher-order interactions in multilayer systems can cause multiple abrupt synchronization transitions. This study develops a framework to explain these complex dynamics in real-world networks.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Globally coupled systems with higher-order interactions exhibit first-order synchronization transitions.
  • Multilayer networks are prevalent in natural and artificial systems.

Purpose of the Study:

  • To investigate the impact of simplicial complexes on synchronization dynamics in multilayer systems.
  • To develop an analytical framework for understanding multiple synchronization transitions.

Main Methods:

  • Utilized the Ott-Antonsen approach.
  • Developed an analytical framework for simplicial complexes on multilayer systems.
  • Reduced high-dimensional equations to a low-dimensional manifold.

Main Results:

  • Discovered that simplicial complexes in multilayer systems can lead to multiple basins of attraction.
  • Observed multiple abrupt first-order transitions to (de)synchronization.
  • Explained the origin and stability of various dynamical states, including multiple synchronization transitions.

Conclusions:

  • Simplicial complexes in multilayer systems introduce rich dynamical behaviors, including multiple synchronization transitions.
  • The analytical framework provides a thorough understanding of these complex dynamics.
  • Findings are crucial for comprehending higher-order interactions in real-world networks like the brain and social systems.