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Anomalous diffusion and long-range memory in the scaled voter model.

Rytis Kazakevičius1, Aleksejus Kononovicius1

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Summary
This summary is machine-generated.

We introduce a scaled voter model with time-dependent herding behavior. This model, driven by scaled Brownian motion, offers insights into complex systems and may substitute bounded fractional Brownian motion.

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Area of Science:

  • Statistical Physics
  • Complex Systems Modeling
  • Mathematical Biology

Background:

  • The noisy voter model is a fundamental tool for studying opinion dynamics.
  • Understanding time-dependent herding behavior is crucial for modeling complex social and biological systems.
  • Existing models often lack the flexibility to capture evolving herding intensities.

Purpose of the Study:

  • To analyze a scaled voter model with power-law time-dependent herding intensity.
  • To derive analytical expressions for the model's moments and first passage time distribution.
  • To investigate the model's long-range memory properties and steady-state behavior.

Main Methods:

  • Analytical derivation of time evolution for the first and second moments.
  • Development of an analytical approximation for the first passage time distribution.
  • Numerical simulations to validate analytical results and explore model dynamics.

Main Results:

  • The scaled voter model simplifies to a noisy voter model driven by scaled Brownian motion.
  • Analytical expressions for model moments and first passage time distribution were obtained.
  • Numerical simulations confirmed analytical findings and revealed long-range memory indicators.

Conclusions:

  • The scaled voter model accurately captures time-dependent herding phenomena.
  • Despite being a Markov process, the model exhibits long-range memory characteristics.
  • The model's steady-state distribution aligns with bounded fractional Brownian motion, suggesting its utility as a substitute.