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Diffusive majority-vote model.

J R S Lima1, F W S Lima1, T F A Alves1

  • 1Departamento de Física, Universidade Federal do Piauí, 57072-970, Teresina - PI, Brazil.

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Summary
This summary is machine-generated.

This study introduces a new model for consensus formation in mobile populations. Faster diffusing individuals gain dominance, influencing the collective opinion in this reaction-diffusion process.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Mathematical Modeling

Background:

  • Consensus formation is crucial in social dynamics and biological systems.
  • Understanding opinion dynamics in mobile populations requires models that incorporate movement and interaction.
  • Existing models often simplify population mobility or interaction rules.

Purpose of the Study:

  • To introduce a novel stochastic reaction-diffusion process for consensus formation in nonsedentary populations.
  • To investigate the influence of diffusion rates and an external field on consensus dynamics.
  • To analyze the phase transitions and dominant factors in collective opinion formation.

Main Methods:

  • A diffusive version of the majority-vote model was developed.
  • The model incorporates two stages: spin-state diffusion and local majority-vote updates.
  • Varying diffusion probabilities (D+, D-) simulated an external magnetic field effect.

Main Results:

  • A consensus formation phase emerges above a critical concentration threshold.
  • Unequal diffusion probabilities (simulating an external field) lead to discontinuous phase transitions.
  • Individuals with higher diffusion rates dominate the final collective opinion.

Conclusions:

  • The developed reaction-diffusion model effectively captures consensus formation in mobile populations.
  • Diffusion asymmetry is a key factor driving opinion dominance and phase transitions.
  • The model provides insights into how mobility influences collective behavior and opinion dynamics.