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This study explores adaptive multilayer networks with higher-order interactions. Introducing order parameter adaptations reveals complex, tiered synchronization transitions and multiple pathways to collective behavior.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Real-world networks exhibit adaptive behavior and simultaneous interactions.
  • Higher-order interactions are crucial in many complex systems.
  • Understanding adaptive dynamics in multilayer networks is essential.

Purpose of the Study:

  • Investigate the dynamics of adaptive multilayer networks with higher-order interactions.
  • Analyze the influence of order parameter adaptation on synchronization routes.
  • Explore the impact of linear and nonlinear adaptation functions.

Main Methods:

  • Modeling adaptive multilayer networks of Kuramoto oscillators.
  • Analyzing dynamics with pairwise and higher-order interactions.
  • Studying bifurcations and basins of attraction for adaptive systems.

Main Results:

  • Discovered tiered transitions to synchronization with linear adaptation.
  • Observed continuous, abrupt, and multiple routes to synchronization.
  • Identified three nonlinear adaptation-induced tiered transitions: continuous, discontinuous, and hysteretic.

Conclusions:

  • Order parameter adaptations significantly influence dynamics in higher-order multilayer networks.
  • Adaptive interactions can create multistability and alter synchronization pathways.
  • The study provides insights into synchronization phenomena in complex adaptive systems.