Record-Breaking Avalanches in Driven Threshold Systems

TL;DR

This paper investigates record-breaking avalanches in driven nonlinear threshold models, revealing how their statistics differ from independent random events and highlighting the influence of model parameters on avalanche correlations.

Contribution

It introduces analytical and numerical analysis of record-breaking avalanche statistics across multiple cellular automata, emphasizing deviations from i.i.d. behavior and the role of correlations.

Findings

Record-breaking avalanche statistics differ from i.i.d. models.

The OFC model shows strong dependence on conservation parameters.

Avalanches exhibit significant spatio-temporal correlations.

Abstract

Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where slow buildup of energy is punctuated by an abrupt release of energy through avalanche events which usually follow scale invariant statistics. From the simulations of these systems it is possible to extract sequences of record-breaking avalanches, where each subsequent record-breaking event is larger in magnitude than all previous events. In the present work, several cellular automata are analyzed among them the sandpile model, Manna model, Olami-Feder-Christensen (OFC) model, and the forest-fire model to investigate the record-breaking statistics of model avalanches which exhibit temporal and spatial correlations. Several statistical measures of record-breaking events are derived analytically and confirmed through numerical simulations. The statistics of record-breaking avalanches for the four models are compared to that of record-breaking events extracted from the sequences of independent identically distributed (\emph{i.i.d.}) random variables. It is found that the statistics of record-breaking avalanches for the above cellular automata exhibit behavior different from that observed for \emph{i.i.d.} random variables which in turn can be used to characterize complex spatio-temporal dynamics. The most pronounced deviations are observed in the case of the OFC model with a strong dependence on the conservation parameter of the model. This indicates that avalanches in the OFC model are not independent and exhibit spatio-temporal correlations.