Relaxation Oscillations in Model Sandpiles

TL;DR

This paper presents a simple one-dimensional sandpile model that exhibits both self-organized criticality and relaxation oscillations, depending on the driving method, aligning with experimental observations of real sandpiles.

Contribution

It introduces a minimalistic model capable of reproducing key behaviors of real sandpiles, including criticality and oscillations, with robustness to rule modifications.

Findings

Model exhibits relaxation oscillations and criticality

Oscillations depend on driving method

Robust to rule modifications

Abstract

We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven, mirroring the experimental situation for real sandpiles. The relaxation oscillations are robust with respect to minor modifications of the avalanche rules, including the application of probabilistic rules.