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Federico Vazquez1, Víctor M Eguíluz, Maxi San Miguel

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain. federico@ifisc.uib.es

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Summary
This summary is machine-generated.

We studied a coevolution voter model on complex networks. A critical transition was found between active and frozen network phases, dependent on average network degree.

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Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • Voter models are used to study opinion dynamics.
  • Coevolution models incorporate network structure changes.
  • Phase transitions are critical points where system properties change dramatically.

Purpose of the Study:

  • To investigate the coevolution voter model on complex networks.
  • To identify the nature of phase transitions in this model.
  • To analyze the factors influencing the transition and its dynamics.

Main Methods:

  • Mean-field approximation to analyze the model.
  • Analysis of finite-size systems to understand phase behavior.
  • Studying the model as an equivalent random walk to characterize transition dynamics.

Main Results:

  • An absorbing phase transition from an active to a frozen state was identified.
  • The critical transition point depends solely on the average degree of the network.
  • In finite systems, phases correspond to connected (active) and fragmented (frozen) networks.
  • The transition time scale diverges near the critical point, following a power law.

Conclusions:

  • The coevolution voter model exhibits a clear phase transition driven by network structure.
  • Network connectivity plays a crucial role in determining the system's final state.
  • The model provides insights into phenomena like opinion fragmentation and network fragmentation.