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The noisy voter model on complex networks.

Adrián Carro1, Raúl Toral1, Maxi San Miguel1

  • 1IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain.

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We developed a new analytical method for complex network models, revealing how network structure, specifically degree heterogeneity, influences system behavior and critical transitions. This method allows inferring network properties from aggregate observations.

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Network Science

Background:

  • Traditional mean-field theories often oversimplify complex network dynamics.
  • Stochastic, binary-state models are crucial for understanding phenomena like opinion dynamics and epidemic spread.
  • The role of network heterogeneity beyond average connectivity is not fully understood.

Purpose of the Study:

  • To introduce a novel analytical method for studying stochastic, binary-state models on complex networks.
  • To investigate the impact of network degree distribution, particularly heterogeneity, on model behavior.
  • To explore the potential for inferring network properties from macroscopic system observations.

Main Methods:

  • Developed an analytical approach using an annealed approximation for uncorrelated networks.
  • Treated network structure as parametric heterogeneity.
  • Applied the method to the noisy voter model to analyze dependencies on degree distribution averages.

Main Results:

  • The method successfully captures dependencies beyond the mean degree, including complex averages.
  • Degree heterogeneity significantly influences the critical point of noise-induced transitions, local ordering, and temporal correlations.
  • Temporal correlation functions provide a means to infer degree heterogeneity from aggregate system behavior.

Conclusions:

  • The proposed analytical method offers a more nuanced understanding of stochastic models on heterogeneous networks.
  • Degree heterogeneity is a critical factor affecting system dynamics and transitions.
  • Observing macroscopic behavior can reveal underlying network structural properties, valuable for systems with limited measurement capabilities.