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Ice sheets appeared in the northern hemisphere around 3 million years ago andglacial-interglacial cycles have paced Earth's climate since then. Superimposedon these long glacial cycles comes an intricate pattern of millennial andsub-millennial variability, including Dansgaard-Oeschger and Heinrich events.There are numerous theories about theses oscillations. Here, we review a numberof them in order to draw a parallel between climatic concepts and dynamicalsystem concepts, including, in particular, the relaxation oscillator,excitability, slow-fast dynamics and homoclinic orbits. Namely, almost alltheories of ice ages reviewed here feature a phenomenon of synchronisationbetween internal climate dynamics and the astronomical forcing. However, thesetheories differ in their bifurcation structure and this has an effect on theway the ice age phenomenon could grow 3 million years ago. All theories onrapid events reviewed here rely on the concept of a limit cycle in the oceancirculation, which may be excited by changes in the surface freshwater surfacebalance. The article also reviews basic effects of stochastic fluctuations onthese models, including the phenomenon of phase dispersion, shortening of thelimit cycle and stochastic resonance. It concludes with a more personalstatement about the potential for inference with simple stochastic dynamicalsystems in palaeoclimate science.  Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages,Dansgaard-Oeschger events

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Oscillators and relaxation phenomena in Pleistocene climate theory