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This study explores the noisy voter model under changing environments, revealing new polarized and heterogeneous states. It also shows how external influencers create multipeak distributions in opinion dynamics.

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Area of Science:

  • Statistical Physics
  • Computational Social Science
  • Mathematical Biology

Background:

  • The noisy voter model is a key framework for understanding opinion dynamics and social influence.
  • Understanding how external factors and environmental fluctuations affect consensus formation is crucial.

Purpose of the Study:

  • To investigate the stationary states of noisy voter models with fluctuating parameters.
  • To analyze the emergence of polarized and heterogeneous states under dynamic environmental conditions.
  • To examine the impact of external influencers on opinion distribution and stationary states.

Main Methods:

  • Individual-based simulations to model agent interactions.
  • Analytical approximations using piecewise-deterministic Markov processes (PDMP).
  • Linear-noise approximation to capture intrinsic stochasticity.
  • Development of a numerical scheme for PDMPs with multiple environmental states.

Main Results:

  • Identified a novel phase exhibiting polarized and heterogeneous states when the herding-to-noise ratio fluctuates.
  • Demonstrated the emergence of multipeak stationary distributions due to external influencers.
  • Validated analytical findings with simulation results.

Conclusions:

  • Environmental fluctuations and external influencers significantly alter opinion dynamics in the noisy voter model.
  • The study provides a theoretical and computational framework for analyzing complex social systems.
  • New insights into the formation of diverse and polarized opinions in populations.