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Time-Delay Induced Dimensional Crossover in the Voter Model.

Mina Kim1, Jae Dong Noh1,2

  • 1Department of Physics, University of Seoul, Seoul 02504, Korea.

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Summary
This summary is machine-generated.

We studied the voter model with time delays, finding it mirrors random walker behavior. Time delays cause a dimensional crossover in ordering dynamics, transitioning from higher to lower dimensions over time.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Dynamical processes

Background:

  • The voter model is a fundamental tool for studying opinion dynamics and social consensus.
  • Understanding how time delays influence these dynamics is crucial for realistic modeling.

Purpose of the Study:

  • To investigate the ordering dynamics of the voter model with time-delayed interactions.
  • To establish a theoretical framework connecting time delays to dimensional crossovers in dynamical systems.

Main Methods:

  • Equivalence established between the voter model dynamics and a first passage problem of a random walker.
  • Analytical derivation of scaling properties and crossover timescales.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Time-delayed voter model dynamics are equivalent to a random walker in a (d+1)-dimensional strip.
  • Time delays induce a dimensional crossover from (d+1)-dimensional to d-dimensional scaling.
  • Analytical predictions for scaling behavior and crossover times confirmed by simulations.

Conclusions:

  • Time delays fundamentally alter the scaling behavior of the voter model.
  • The random walker analogy provides a powerful tool for analyzing delayed dynamical systems.
  • This work offers insights into collective behavior influenced by interaction delays.