Abstract

The use of critical slowing down as an early warning indicator for regime switching in observations from noisy dynamical systems and models has been widely studied and implemented in recent years. Some systems, however, have been shown to avoid critical slowing down prior to a transition between equilibria (Ditlevsen and Johnsen 2010; Hastings and Wysham Ecology Letters 13(4):464–472 2010). Possible explanations include a non-smooth potential driving the dynamic (Hastings and Wysham Ecology Letters 13(4):464–472 2010) or large perturbations driving the system out of the initial basin of attraction (Boettiger and Batt 2018). In this paper, we discuss a phenomenon analogous to critical slowing down, where a slow parameter change leads to a high likelihood of a regime shift and creates signature warning signs in the statistics of the process’s sample paths. This effect, which we dub “critical speeding up,” is demonstrated using a simple population model exhibiting an Allee effect. In short, if a basin of attraction is compressed under a parameter change then the potential well steepens, leading to a drop in the time series’ variance and autocorrelation; precisely the opposite warning signs exhibited by critical slowing down. The fact that either falling or rising variance / autocorrelation can indicate imminent state change should underline the need for reliable modeling of any empirical system where one desires to forecast regime change.

中文翻译：

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紧急加速是随机政权转移的预警信号

摘要

近年来，在噪声动态系统和模型的观测中，使用临界减速作为状态切换的预警指标已得到广泛研究和实施。但是，有些系统已显示出在平衡之间过渡之前避免了关键的减速（Ditlevsen和Johnsen，2010； Hastings和Wysham Ecology Letters 13（4）：464-472 2010）。可能的解释包括驱动动力的非平稳潜力（Hastings and Wysham Ecology Letters 13（4）：464-472 2010）或大扰动使系统脱离了最初的吸引力盆地（Boettiger和Batt 2018））。在本文中，我们讨论了一种类似于临界减速的现象，其中缓慢的参数更改会导致状态转换的可能性很高，并会在过程的样本路径统计信息中创建签名警告信号。我们使用一种显示Allee效应的简单人口模型来证明这种效应，我们将其称为“临界加速”。简而言之，如果一个吸引盆在参数变化下被压缩，那么势阱会变陡，导致时间序列的方差和自相关下降；严格的减速显示出完全相反的警告信号。方差/自相关下降或上升可以表明即将发生状态变化，这一事实应强调需要对希望预测政权变化的任何经验系统进行可靠建模的需求。