Abstract Glacial-interglacial cycles are global climatic changes which have characterised the last 3 million years. The eight latest glacial-interglacial cycles represent changes in sea level over 100 m, and their average duration was around 100 000 years. There is a long tradition of modelling glacial-interglacial cycles with low-order dynamical systems. In some of these models, the cyclic phenomenon is caused by non-linear interactions between components of the climate system, which generate a limit cycle. Other models incorporate the established Milankovitch theory according to which changes in Earth’s orbit and obliquity force variations in ice volume and ice sheet extent along with, either directly or indirectly, variations in other variables of the climate system. One then distinguishes the strong interpretation, in which the astronomical forcing is necessary to generate glacial-interglacial cycles, from the weak interpretation, in which the astronomical forcing synchronises a limit cycle. The purpose of the present contribution is to consider specifically the effects of stochastic forcings. Indeed, the trajectories obtained in presence of stochastic fluctuations are not necessarily noised-up versions of the deterministic trajectories. They may follow pathways which have no analogue in the deterministic version of the model. Our purpose is to demonstrate the mechanisms by which stochastic excitation may generate such large-scale oscillations, sometimes with an intermittent character. To this end, we consider a series of models previously introduced in the literature, starting with autonomous models with two variables, and then three variables. The properties of stochastic trajectories are understood by reference to the bifurcation diagrams, the vector field, and a method called stochastic sensitivity analysis. We then introduce models accounting for the Milankovitch forcing, and distinguish forced and synchronised ice-age scenarios. We show again how noise may generate trajectories which have no immediate analogue in the deterministic model. We conclude on a general reflection on the interest of this research and its potential applications on a wide range of climatic phenomena.

中文翻译：

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非线性气候动力学：从确定性行为到随机兴奋性和混沌

摘要 冰期-间冰期循环是过去300 万年来全球气候变化的特征。8 个最新的冰期-间冰期循环代表了 100 m 以上的海平面变化，平均持续时间约为 100 000 年。用低阶动力系统模拟冰期-间冰期循环有着悠久的传统。在其中一些模型中，循环现象是由气候系统组成部分之间的非线性相互作用引起的，这会产生极限循环。其他模型结合了已建立的米兰科维奇理论，根据该理论，地球轨道的变化以及冰体积和冰盖范围的倾斜力变化，以及气候系统其他变量的直接或间接变化。然后区分强解释，其中天文强迫是产生冰期-间冰期循环所必需的，从弱解释来看，其中天文强迫同步了一个极限循环。本论文的目的是专门考虑随机强迫的影响。事实上，在存在随机波动的情况下获得的轨迹不一定是确定性轨迹的噪声版本。它们可能遵循在模型的确定性版本中没有类似物的路径。我们的目的是展示随机激励可能产生如此大规模振荡的机制，有时具有间歇性特征。为此，我们考虑了之前在文献中介绍的一系列模型，从具有两个变量的自治模型开始，然后是三个变量。通过参考分岔图、矢量场和称为随机灵敏度分析的方法可以理解随机轨迹的特性。然后我们介绍解释米兰科维奇强迫的模型，并区分强迫和同步冰河时代情景。我们再次展示了噪声如何产生在确定性模型中没有直接类似物的轨迹。我们总结了对这项研究的兴趣及其对广泛气候现象的潜在应用的普遍反思。我们再次展示了噪声如何产生在确定性模型中没有直接类似物的轨迹。我们总结了对这项研究的兴趣及其对广泛气候现象的潜在应用的总体反思。我们再次展示了噪声如何产生在确定性模型中没有直接类似物的轨迹。我们总结了对这项研究的兴趣及其对广泛气候现象的潜在应用的总体反思。