Sandpile on scale-free networks.

Area of Science:

• Complex systems
• Network science
• Statistical physics

Background:

• The Bak-Tang-Wiesenfeld sandpile model is a classic model for self-organized criticality.
• Scale-free networks exhibit heterogeneous degree distributions, impacting system dynamics.
• Understanding avalanche dynamics is crucial for characterizing complex systems.

Purpose of the Study:

• To investigate avalanche dynamics in the Bak-Tang-Wiesenfeld sandpile model on scale-free networks.
• To analyze how heterogeneous node thresholds, based on node degree, influence avalanche behavior.
• To derive analytic expressions for critical exponents and compare them with numerical simulations.

Main Methods:

• Simulation of the Bak-Tang-Wiesenfeld sandpile model on scale-free networks.
• Analysis of avalanche size distribution and identification of power-law behavior.
• Application of multiplicative branching process theory to derive analytic exponents.

Main Results:

• The avalanche size distribution follows a power law with exponent tau.
• Analytic expressions for tau and the dynamic exponent z were derived as functions of the scale-free network's degree exponent gamma.
• For 23, mean-field values tau=1.5 and z=2.0 were found, with logarithmic corrections at gamma=3.
• A uniform threshold case reduces exponents to mean-field values.

Conclusions:

• The study provides a comprehensive analytic understanding of avalanche dynamics on scale-free networks.
• Node degree heterogeneity significantly influences critical exponents in sandpile models.
• The findings offer insights into the behavior of complex systems with heterogeneous structures.