Alkhayuon Hassan, Tyson Rebecca C, Wieczorek Sebastian
University College Cork, School of Mathematical Sciences, Western Road, Cork T12 XF62, Ireland.
CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, British Columbia, Canada.
Proc Math Phys Eng Sci. 2021 Oct;477(2254):20210059. doi: 10.1098/rspa.2021.0059. Epub 2021 Oct 6.
We identify the as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator-prey cycle to extinction in two paradigmatic predator-prey models with an Allee effect. Our analysis of these examples uncovers a counterintuitive behaviour, which we call phase tipping or , where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of for attracting limit cycles. This concept provides a general framework to analyse and identify easily testable criteria for the occurrence of phase tipping in externally forced systems, and can be extended to more complicated attractors.
我们确定 为在随时间变化的外部条件下循环系统中临界点（临界转变）的一个新的关键因素。作为一个例子，我们考虑当代气候变率如何在具有阿利效应的两个典型捕食 - 猎物模型中引发从捕食 - 猎物循环到灭绝的转变。我们对这些例子的分析揭示了一种违反直觉的行为，我们称之为相位转变或 ，其中只有从循环的某些阶段才会发生向灭绝的转变。为了解释这种行为，我们将全局动力学与集合论相结合，并引入了吸引极限环的 概念。这个概念提供了一个通用框架，用于分析和确定外部强迫系统中相位转变发生的易于测试的标准，并且可以扩展到更复杂的吸引子。
