Abstract
Self-organized criticality (SOC) successfully describes power law behaviour of size distribution in many natural phenomena. However, it does not consider time correlations between events and therefore it is unable to reproduce the time occurrence behaviour, namely the inter-event time distribution, extremely relevant for many problems. 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. We apply the model to the study of earthquake occurrence and we obtain, without any parameter tuning, excellent agreement with inter-event time and magnitude distributions from the Southern California Catalog.