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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.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|April 24, 2002

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.

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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.

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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.