MacLaren Neil G, Aihara Kazuyuki, Masuda Naoki
Department of Mathematics, State University of New York at Buffalo, New York, NY 14260-2900, USA.
International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Bunkyo-ku, Japan.
J R Soc Interface. 2025 May;22(226):20240696. doi: 10.1098/rsif.2024.0696. Epub 2025 May 7.
Early warning signals (EWSs) for complex dynamical systems aim to anticipate tipping points before they occur. While signals computed from time-series data, such as temporal variance, are useful for this task, they are costly to obtain in practice because they need many samples over time to calculate. Spatial EWSs use just a single sample per spatial location and aggregate the samples over space rather than time to try to mitigate this limitation. However, although many complex systems in nature and society form diverse networks, the performance of spatial EWSs is mostly unknown for general networks because the vast majority of studies of spatial EWSs have been on regular lattice networks. Therefore, we have carried out a comprehensive investigation of six major spatial EWSs on various networks. We find that the winning EWS depends on tipping scenarios, although the coefficient of variation and spatial skewness tend to outperform alternative EWSs. We also find that spatial EWSs behave in a drastically different manner between the square lattice and complex networks and tend to be more reliable for the latter than the former. The present results encourage further studies of spatial EWSs on complex networks.
复杂动力系统的早期预警信号（EWS）旨在预测临界点在发生之前出现。虽然从时间序列数据计算出的信号，如时间方差，对于这项任务很有用，但在实践中获取它们成本很高，因为它们需要随时间的许多样本进行计算。空间EWS在每个空间位置仅使用单个样本，并在空间而非时间上汇总样本，以试图减轻这一限制。然而，尽管自然界和社会中的许多复杂系统形成了多样的网络，但对于一般网络，空间EWS的性能大多未知，因为绝大多数关于空间EWS的研究都是针对规则晶格网络。因此，我们对各种网络上的六种主要空间EWS进行了全面研究。我们发现，尽管变异系数和空间偏度往往比其他EWS表现更好，但获胜的EWS取决于临界点情况。我们还发现，空间EWS在方形晶格和复杂网络之间的行为方式截然不同，并且对于后者往往比前者更可靠。目前的结果鼓励对复杂网络上的空间EWS进行进一步研究。
