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Symmetries and cluster synchronization in multilayer networks.

Fabio Della Rossa1,2, Louis Pecora3, Karen Blaha1

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We analyzed symmetries in multilayer networks to understand cluster synchronization. Dependent layer symmetries, involving nodes across layers, uniquely impact synchronization stability, confirmed by analog experiments.

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Area of Science:

  • Complex systems science
  • Network science
  • Physics

Background:

  • Real-world systems like epidemiology and economics are often modeled as multilayer networks.
  • Understanding synchronization phenomena in these complex networks is crucial for various scientific and engineering domains.

Purpose of the Study:

  • To define and compute symmetries in multilayer networks.
  • To investigate the emergence and stability of cluster synchronization in these networks.
  • To differentiate between independent and dependent layer symmetries and their impact.

Main Methods:

  • Definition and computation of multilayer network symmetries.
  • Analysis of cluster synchronization stability using a Master Stability Function.
  • Decoupling the stability problem into independent blocks.
  • Validation through analog experiments with electronic oscillators.

Main Results:

  • Distinction between independent layer symmetries and dependent layer symmetries.
  • Dependent layer symmetries exhibit a unique structure affecting cluster synchronization stability.
  • The Master Stability Function approach effectively assesses stability across different network blocks.

Conclusions:

  • Symmetries play a critical role in the synchronization dynamics of multilayer networks.
  • Dependent layer symmetries present unique challenges and characteristics for achieving stable cluster synchronization.
  • The theoretical framework is validated by experimental results, confirming its applicability to real-world systems.