Memory in Self Organized Criticality

Abstract

Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like statistics, i.e. exponential behaviour in the inter-event time distribution, in contrast with experimental observations. We present a SOC model with memory: events are nucleated not only as a consequence of the instantaneous value of the local field with respect to the firing threshold, but on the basis of the whole history of the system. The model is able to reproduce the complex behaviour of inter-event time distribution, in excellent agreement with experimental seismic data.

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• The Weibull - log Weibull Transition of the Inter-occurrence time statistics in the two-dimensional Burridge-Knopoff Earthquake model
• Spatiotemporal Memory in a Diffusion-Reaction System