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[en] The most pronounced mode of climate variability during the last glacial period are the so-called Dansgaard–Oeschger events. There is no consensus of the underlying dynamical mechanism of these abrupt climate changes and they are elusive in most simulations of state-of-the-art coupled climate models. There has been significant debate over whether the climate system is exhibiting self-sustained oscillations with vastly varying periods across these events, or rather noise-induced jumps in between two quasi-stable regimes. In previous studies, statistical model comparison has been employed to the NGRIP ice core record from Greenland in order to compare different classes of stochastic dynamical systems, representing different dynamical paradigms. Such model comparison studies typically rely on accurately reproducing the observed records. We aim to avoid this due to the large amount of stochasticity and uncertainty both on long and short time scales in the record. Instead, we focus on the most important qualitative features of the data, as captured by summary statistics. These are computed from the distributions of waiting times in between events and residence times in warm and cold regimes, as well as the stationary density and the autocorrelation function. We perform Bayesian inference and model comparison experiments based solely on these summary statistics via Approximate Bayesian Computation. This yields an alternative approach to existing studies that helps to reconcile and synthesize insights from Bayesian model comparison and qualitative statistical analysis.

[en] Graphical abstract: The ice age dynamics have existed in two modes of operation, the 41-kyr periods until 1 million years ago and the approximately 100-kyr periods of the present state. These correspond to two different stability diagrams, where the approximate periodicity of the latter period could be due to a generalized stochastic resonance. - Abstract: Understanding the dynamics of ice ages has been a major challenge in climate research for more than a century. The cycles are thus attributed to the climatic response of the orbital changes in the incoming solar radiation to the Earth. However, these changes in the forcing are too small to explain the observed climate variations as simple linear responses, thus non-linear amplifications of the orbital forcing are necessary to account for the glacial cycles. Stochastic resonance was proposed by Benzi et al. to describe this scenario. However, there are several shortcomings in the description of the glacial cycles as a simple stochastic resonance. In order to account for the non-periodic nature of the ice age cycles, especially the shift 1 million years ago from 41-kyr ice age cycles to the present approximately 100-kyr ice age cycles, a non-trivial extension of the notion of a stochastic resonance is needed.

[en] Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the fast subsystem) and associated fast dynamics, parametrized by the slow variables. Using a distinguished parameter approach we are able to classify bifurcations for one fast and one slow variable. Some of these bifurcations are associated with the critical set losing manifold structure. We also conjecture a list of generic bifurcations of the critical set for one fast and two slow variables. We further consider how the bifurcations of the critical set can be associated with generic bifurcations of attracting relaxation oscillations under an appropriate singular notion of equivalence. (paper)