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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • Voter models are used to study opinion dynamics on networks.
  • Multilayer networks consist of multiple interacting layers.
  • Network evolution and dynamics are often studied independently.

Purpose of the Study:

  • To investigate the impact of differing topological temporal scales in multilayer networks on opinion dynamics.
  • To introduce and analyze a coevolution voter model in a multiplex network framework.
  • To identify novel transition phenomena and their characteristics.

Main Methods:

  • Development of a coevolution voter model for two coupled network layers.
  • Analysis of network dynamics under varying interlayer coupling and topological time scales.
  • Mapping of dynamics to a single-layer model when time scales are equal.
  • Identification of transition signatures, such as component growth.

Main Results:

  • When time scales are equal, dynamics resemble a single-layer model with an effective average degree, preserving the absorbing-fragmentation transition.
  • The critical value for this transition increases with the degree of multiplexing.
  • When time scales differ, an anomalous transition termed 'shattered fragmentation' occurs.
  • Shattered fragmentation is characterized by a layer splitting into two large, oppositely-aligned components and numerous isolated nodes.
  • The number of components serves as a signature for this anomalous transition.
  • The critical interlayer coupling to prevent fragmentation in a connected layer was determined.

Conclusions:

  • The temporal dynamics of individual layers significantly influence collective behavior in multilayer networks.
  • Shattered fragmentation represents a new class of phase transitions in complex systems.
  • Understanding interlayer coupling is crucial for maintaining network integrity and preventing fragmentation.