Shapoval Alexander, Savostianova Dayana, Shnirman Mikhail
Department of Mathematics and Computer Science of the University of Łódż, Banacha 22, Łódż 90-238, Poland.
Gran Sasso Science Institute, Crispi 7, 67100 L'Aquila, Italy.
Chaos. 2022 Aug;32(8):083130. doi: 10.1063/5.0102019.
Substantiated explanations of the unpredictability regarding sandpile models of self-organized criticality (SOC) gave way to efficient forecasts of extremes in a few models. The appearance of extremes requires a preparation phase that ends with general overloading of the system and spatial clustering of the local stress. Here, we relate the predictability of large events to the system volume in the Manna and Bak-Tang-Wiesenfeld sandpiles, which are basic models of SOC. We establish that in the Manna model, the events located to the right of the power-law segment of the size-frequency relationship are predictable and the prediction efficiency is described by the universal linear dependence on the event size scaled by a power-law function of the lattice volume. Our scaling-based approach to predictability contributes to the theory of SOC and may elucidate the forecast of extremes in the dynamics of such systems with SOC as neuronal networks and earthquakes.
对自组织临界性（SOC）沙堆模型不可预测性的合理解释，在一些模型中让位于对极端情况的有效预测。极端情况的出现需要一个准备阶段，该阶段以系统的普遍过载和局部应力的空间聚集结束。在这里，我们将曼纳（Manna）和巴克 - 唐 - 维森费尔德（Bak-Tang-Wiesenfeld）沙堆（SOC的基本模型）中重大事件的可预测性与系统体积联系起来。我们确定，在曼纳模型中，位于大小 - 频率关系幂律段右侧的事件是可预测的，并且预测效率由对事件大小的通用线性依赖来描述，该事件大小由晶格体积的幂律函数缩放。我们基于标度的可预测性方法有助于SOC理论，并可能阐明具有SOC的此类系统（如神经网络和地震）动力学中极端情况的预测。
