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Synchronization in adaptive higher-order networks.

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Summary
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This study introduces adaptive higher-order networks to model complex systems with group interactions. It reveals conditions for stable synchronization, showing how group dynamics and adaptation influence system behavior.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Nonlinear Dynamics

Background:

  • Complex systems often exhibit group interactions that change over time.
  • Existing adaptive network models primarily focus on pairwise interactions, neglecting group dynamics.

Purpose of the Study:

  • To develop a general framework for adaptive higher-order networks that incorporates both adaptivity and group interactions.
  • To identify the conditions necessary for stable global synchronization in such systems.

Main Methods:

  • Proposed a general framework for adaptive higher-order networks.
  • Analyzed systems with adaptive pairwise interactions and then extended to adaptive higher-order interactions.
  • Utilized the master stability equation to derive conditions for synchronization.

Main Results:

  • Demonstrated the existence of global synchronization in adaptive higher-order networks.
  • Identified necessary conditions for stable synchronous states, separating dynamical and structural properties.
  • Showcased findings using coupled generalized Kuramoto oscillators with phase lag.

Conclusions:

  • The interplay of group interactions and adaptive connectivity creates stability regions, enabling transitions between synchronization and desynchronization.
  • Higher-order adaptation significantly impacts synchronization stability compared to constant higher-order interactions.