Self-Organized Criticality in Non-conserved Systems

TL;DR

This paper investigates how self-organized criticality arises in non-conserved systems, revealing the role of boundary conditions and synchronization mechanisms through simplified models and detailed analysis.

Contribution

It demonstrates the emergence of self-organized criticality in non-conserved systems and links it to synchronization phenomena, providing a simplified model for explanation.

Findings

Open boundaries induce self-organized regions.

Avalanche-distribution exponent depends on conservation parameter.

Synchronization explains critical behavior in non-conserved models.

Abstract

The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized'' region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter $\alpha$ is examined.