动力系统中的极端事件与随机游走
Extreme events in dynamical systems and random walkers: A review
摘要：
极端事件由于其在从金融到气候学的各种背景下的极端重要性而引起研究人员的关注。这使得这些经常发生的事件成为跨学科研究的焦点。最近的进展提供了一个全面的审查，以捕捉最近的改进，从动力系统和随机游走的角度来分析这种非常高振幅的事件。我们强调，在细节，机制负责出现这样的事件在复杂系统。已经详细阐述了导致极端事件发生的几种机制，调查了导致极端事件的不稳定性的来源。此外，我们讨论了从两个不同的背景下，使用动态不稳定性和基于数据的机器学习算法的极端事件的预测。跟踪相空间中的不稳定性并不总是可行的，对极端事件动态的精确了解并不一定有助于预测极端事件。此外，在大多数高维系统的研究中，只有少数自由度参与极端事件的形成。因此，通过机器学习进行预测的重要性是非常重要的，特别是对于那些模型的控制方程明确不可用的情况。此外，复杂网络上的随机游动可以代表多个运输过程，游动者流量的不确定性超过一个给定的阈值可以描述极端事件。我们揭示了随机游走的理论研究，它们在减少极端事件方面具有巨大的应用潜力。我们涵盖了可能的控制策略，这可能有助于缓解物理情况下的极端事件，如交通堵塞，Web请求的重负载，共享资源的竞争，河流网络中的洪水等等。
英文摘要：
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A comprehensive review of recent progress is provided to capture recent improvements in analyzing such very high-amplitude events from the point of view of dynamical systems and random walkers. We emphasize, in detail, the mechanisms responsible for the emergence of such events in complex systems. Several mechanisms that contribute to the occurrence of extreme events have been elaborated that investigate the sources of instabilities leading to them. In addition, we discuss the prediction of extreme events from two different contexts, using dynamical instabilities and data-based machine learning algorithms. Tracking of instabilities in the phase space is not always feasible and precise knowledge of the dynamics of extreme events does not necessarily help in forecasting extreme events. Moreover, in most studies on high-dimensional systems, only a few degrees of freedom participate in extreme events' formation. Thus, the notable inclusion of prediction through machine learning is of enormous significance, particularly for those cases where the governing equations of the model are explicitly unavailable. Besides, random walks on complex networks can represent several transport processes, and exceedances of the flux of walkers above a prescribed threshold may describe extreme events. We unveil the theoretical studies on random walkers with their enormous potential for applications in reducing extreme events. We cover the possible controlling strategies, which may be helpful to mitigate extreme events in physical situations like traffic jams, heavy load of web requests, competition for shared resources, floods in the network of rivers, and many more.
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