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Anomalous diffusion in nonlinear transformations of the noisy voter model
Rytis Kazakevičius1, Aleksejus Kononovicius1
1Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257 Vilnius, Lithuania.
Physical Review. E
|April 17, 2021
Summary
The original voter model exhibits ballistic anomalous diffusion. Nonlinear transformations reveal normal and other anomalous diffusion regimes, matching analytical approximations.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Voter models are established tools in interdisciplinary research.
- Previous studies have not explored voter models through the lens of anomalous diffusion.
Purpose of the Study:
- To investigate the voter model's behavior within the framework of anomalous diffusion.
- To identify and characterize different diffusion regimes exhibited by the voter model.
Main Methods:
- Analysis of the original voter model.
- Application of nonlinear transformations to observation variables and time scales.
- Derivation of analytical approximations for raw moment evolution.
- Comparison with numerical simulation results.
Main Results:
- The original voter model demonstrates a ballistic diffusion regime.
- Nonlinear transformations reveal normal and other anomalous diffusion regimes.
- Numerical simulations align with derived analytical approximations for temporal evolution of raw moments.
Conclusions:
- The voter model exhibits diverse anomalous diffusion behaviors.
- Analytical approximations accurately describe the model's dynamics across different regimes.
- This work bridges voter models and anomalous diffusion studies.
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