Self-organized criticality in the olami-feder-christensen model

Area of Science:

• Complex systems
• Statistical physics
• Dynamical systems

Background:

• Self-organized criticality (SOC) is often identified by power-law distributions of system events.
• Finite-size scaling analysis is a common method to infer SOC.
• Traditional methods can be misleading in determining true criticality.

Purpose of the Study:

• To introduce and validate a new method for identifying self-organized criticality using branching rates.
• To re-evaluate the criticality of the Olami-Feder-Christensen (OFC) model.
• To determine the specific conditions under which the OFC model exhibits criticality.

Main Methods:

• Analysis of the branching rate (sigma) of events within a system.
• Application of the branching rate analysis to the Olami-Feder-Christensen model.
• Comparison of results with traditional finite-size scaling methods.

Main Results:

• The branching rate analysis provides a more reliable indicator of criticality than power-law distributions alone.
• The Olami-Feder-Christensen model demonstrates criticality exclusively within its conservative regime.
• Previous conclusions regarding the OFC model's criticality are revised.

Conclusions:

• Branching rate analysis offers a robust alternative for detecting self-organized criticality.
• The Olami-Feder-Christensen model is not universally critical but exhibits criticality under specific conservative conditions.
• This work refines the understanding of criticality in complex systems and specific models.