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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Synchronization in complex networks is a key area of research.
  • Multiplex networks, with multiple interacting layers, are common in real-world systems.
  • Understanding collective behavior in these networks is crucial.

Purpose of the Study:

  • Investigate collective behaviors of Kuramoto oscillators on single-layer and duplex Li networks.
  • Analyze the impact of network topology and inter-layer interactions on synchronization.
  • Compare synchronization dynamics between single-layer and multiplex network architectures.

Main Methods:

  • Utilized Kuramoto oscillator models on single-layer and duplex Li networks.
  • Introduced a total cost restriction for network construction.
  • Analyzed the influence of network topology (regularity) and inter-layer coupling strength on synchronizability.

Main Results:

  • On single-layer Li networks, increased regularity (closer to a lattice) hinders synchronization.
  • Inter-layer interactions in duplex Li networks significantly enhance both inter-layer and global synchronizability.
  • A critical inter-layer coupling strength guarantees inter-layer synchronization.
  • Node degree's influence on synchronization is diminished in duplex networks due to inter-layer effects.

Conclusions:

  • Network topology is critical for synchronization in single-layer systems.
  • Multiplexity and inter-layer coupling are powerful mechanisms for enhancing synchronization.
  • Findings offer insights into collective behaviors in real-world multiplex systems.