Related Experiment Videos
Levy-nearest-neighbors Bak-Sneppen model
R Cafiero1, P De Los Rios, A Valleriani
1PMMH, Ecole Supérieure de Physique et de chimie Industrielles, 10, rue Vaquelin, 75231 Paris, France.
Summary
This study introduces a modified Bak-Sneppen model with a power-law distribution for neighbor selection. Results reveal that model exponents depend on the power-law exponent, omega, and suggest a critical dimension of six.
Area of Science:
- Complex Systems
- Statistical Physics
- Dynamical Systems
Background:
- The Bak-Sneppen (BS) model is a key model for studying self-organized criticality (SOC).
- Previous research focused on nearest-neighbor interactions or high-dimensional behavior.
Purpose of the Study:
- To investigate a generalized random neighbor version of the Bak-Sneppen model.
- To explore the impact of a power-law distribution for neighbor selection on SOC properties.
- To determine the critical dimension of the Bak-Sneppen model.
Main Methods:
- Analysis of a modified Bak-Sneppen model with a probability distribution P(x) ~ x^(-omega) for neighbor selection.
- Examination of how SOC exponents vary with the exponent omega.
- Comparison with existing simulations of the original BS model.
Main Results:
- All exponents characterizing the self-organized critical state depend on the exponent omega.
- The model recovers the standard random nearest-neighbor version as omega approaches 1.
- Results are consistent with high-dimensional simulations of the original BS model.
Conclusions:
- The generalized random neighbor approach provides insights into the BS model's behavior.
- A critical dimension (dc) of 6 is proposed for the Bak-Sneppen model, challenging prior findings.