The forecasting of sudden, irreversible shifts in natural systems is a challenge of great importance, whose realization could allow pre-emptive action to be taken to avoid or mitigate catastrophic transitions, or to help systems adapt to them. In recent years, there have been many advances in the development of such early warning signals. However, much of the current toolbox is based around the tracking of statistical trends and therefore does not aim to estimate the future time scale of transitions or resilience loss. Metric-based indicators are also difficult to implement when systems have inherent oscillations which can dominate the indicator statistics. To resolve these gaps in the toolbox, we use additional system properties to fit parsimonious models to dynamics in order to predict transitions. Here, we consider nearly-one-dimensional systems—higher dimensional systems whose dynamics can be accurately captured by one-dimensional discrete time maps. We show how the nearly one-dimensional dynamics can be used to produce model-based indicators for critical transitions which produce forecasts of the resilience and the time of transitions in the system. A particularly promising feature of this approach is that it allows us to construct early warning signals even for critical transitions of chaotic systems. We demonstrate this approach on two model systems: of phosphorous recycling in a shallow lake, and of an overcompensatory fish population.

中文翻译：

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预测近一维系统中政权转变前的弹性曲线

预测自然系统中突然、不可逆转的变化是一项非常重要的挑战，其实现可以采取先发制人的行动来避免或减轻灾难性转变，或帮助系统适应它们。近年来，此类预警信号的开发取得了许多进展。然而，当前的大部分工具箱都是基于统计趋势的跟踪，因此并不旨在估计未来的转变或弹性损失的时间尺度。当系统具有可支配指标统计数据的固有振荡时，基于度量的指标也难以实施。为了解决工具箱中的这些差距，我们使用额外的系统属性来将简约模型拟合到动力学以预测转换。这里，我们考虑近一维系统——高维系统，其动力学可以被一维离散时间图准确捕获。我们展示了如何使用近一维动态来为关键转变生成基于模型的指标，从而预测系统中的弹性和转变时间。这种方法的一个特别有前途的特点是，它允许我们甚至为混沌系统的关键转变构建早期预警信号。我们在两个模型系统上展示了这种方法：浅湖中的磷循环和过度补偿的鱼类种群。我们展示了如何使用近一维动态来为关键转变生成基于模型的指标，从而预测系统中的弹性和转变时间。这种方法的一个特别有前途的特点是，它允许我们甚至为混沌系统的关键转变构建早期预警信号。我们在两个模型系统上展示了这种方法：浅湖中的磷循环和过度补偿的鱼类种群。我们展示了如何使用近一维动态来为关键转变生成基于模型的指标，从而预测系统中的弹性和转变时间。这种方法的一个特别有前途的特点是，它允许我们甚至为混沌系统的关键转变构建早期预警信号。我们在两个模型系统上展示了这种方法：浅湖中的磷循环和过度补偿的鱼类种群。