Theory and observation tell us that many complex systems exhibit tipping points—thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein–Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator–prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.

中文翻译：

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使用光谱预警信号检测和区分临界点

理论和观察告诉我们，许多复杂系统都表现出临界点——阈值涉及到一个对比鲜明的动态机制的突然和不可逆转的转变。此类事件通常称为临界转换。目前的研究旨在开发关键转变的早期预警信号 (EWS)，以帮助防止生态系统崩溃等不良事件。然而，传统的 EWS 并不表明过渡的类型，因为它们基于临界减速的一般现象。例如，他们可能无法区分振荡的开始（例如 Hopf 分叉）与向远处吸引子的过渡（例如折叠分叉）。此外，传统 EWS 在具有密度相关噪声的系统中不太可靠。已经提出了其他基于功率谱（spectral EWS）的 EWS，但它们依赖于光谱变红，这不会在具有振荡分量的临界跃迁之前发生。在这里，我们使用 Ornstein-Uhlenbeck 理论在每种类型的局部分叉之前推导出 EWS 的解析近似值，从而创建新的光谱 EWS，对跃迁接近度提供更高的灵敏度；对密度相关噪声和分叉类型具有更高的鲁棒性；以及即将到来的转变类型的线索。我们展示了使用种群模型将这些光谱 EWS 与常规 EWS 协同应用的优势，并表明它们在来自捕食者-猎物恒化器实验的数据中的两个不同的 Hopf 分叉之前提供了特征信号。