The Olami-Feder-Christensen model on a small-world topology

TL;DR

This study investigates how small-world network topology influences the self-organized criticality behavior of the Olami-Feder-Christensen earthquake model, revealing critical phenomena and universal scaling in a non-conservative regime.

Contribution

It demonstrates that the OFC model exhibits self-organized criticality on small-world networks, with universal critical exponents across various rewiring probabilities, contrasting with traditional local connectivity models.

Findings

Self-organized criticality persists deep in the non-conservative regime on small-world networks.

Avalanche size distributions follow finite size scaling with universal exponents.

Cutoff of the avalanche size distribution fits a stretched exponential with an exponent approaching one.

Abstract

We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake model of self-organized criticality. In particular, we consider a 2D square lattice and a random rewiring procedure with a parameter $0<p<1$ that allows to tune the interaction graph, in a continuous way, from the initial local connectivity to a random graph. The main result is that the OFC model on a small-world topology exhibits self-organized criticality deep within the non-conservative regime, contrary to what happens in the nearest-neighbors model. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents in a wide range of values of the rewiring probability $p$. The pdf's cutoff can be fitted by a stretched exponential function with the stretching exponent approaching unity within the small-world region.