Dynamic critical approach to self-organized criticality

Area of Science:

• Complex Systems
• Statistical Physics

Background:

• Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
• The Bak-Sneppen (BS) model is a well-established model exhibiting robust SOC behavior.

Purpose of the Study:

• To propose and validate a dynamic scaling ansatz for approaching the SOC regime.
• To determine critical exponents from short-time scaling behavior in the BS model.

Main Methods:

• Extensive computer simulations of the Bak-Sneppen model.
• Analysis of the short-time scaling behavior of site density rho(t).
• Calculation of temporal autocorrelation decay.

Main Results:

• Observed density increase with exponent theta=0.12(2) for rho(t=0)-->0.
• Observed density decay with exponent delta=0.47(2) for rho(t=0)-->1.
• Temporal autocorrelation decay exponent Ca=0.35(2) determined.

Conclusions:

• Dynamically determined critical exponents accurately predict known exponents (z, D, tauALL) of the BS model.
• The proposed ansatz provides a consistent framework for understanding SOC approach.
• Excellent agreement with established SOC regime values validates the findings.