Chaos in Sandpile Models

TL;DR

This paper explores the 'weak chaos' exponent as a potential classification tool for sandpile models, demonstrating its effectiveness in deterministic models and its suppression by stochasticity.

Contribution

It introduces the 'weak chaos' exponent as a characteristic parameter distinguishing different deterministic sandpile models and examines the impact of stochasticity and criticality on this exponent.

Findings

Different 'weak chaos' exponents for BTW and Zhang models suggest different universality classes.

Stochasticity diminishes the effectiveness of 'weak chaos' exponents.

Deviating from the critical point destroys the 'weak chaos' behavior.

Abstract

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.