Quenched disorder, memory, and self-organization

We use a stochastic description of models with a dynamic in quenched disorder to analyze the mechanism of their self-organization to a critical state in terms of memory effects. We introduce a framework to characterize both memory effects and avalanche events which suggests that self-organization can result in general from memory. This issue is settled by the introduction and the analysis of a model that contains explicitly memory and generalizes the corresponding dynamics in quenched disorder. The model displays a rich behavior and self-organized critical properties for a whole range of the exponent that tunes the strength of memory. 1996 The American Physical Society.