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