  It is commonly accepted that the variations of Earth's orbit and obliquity
control the timing of Pleistocene glacial-interglacial cycles. Evidence comes
from power spectrum analysis of palaeoclimate records and from inspection of
the timing of glacial and deglacial transitions. However, we do not know how
tight this control is. Is it, for example, conceivable that random climatic
fluctuations could cause a delay in deglaciation, bad enough to skip a full
precession or obliquity cycle and subsequently modify the sequence of ice ages?
  To address this question, seven previously published conceptual models of ice
ages are analysed by reference to the notion of generalised synchronisation.
Insight is being gained by comparing the effects of the astronomical forcing
with idealised forcings composed of only one or two periodic components. In
general, the richness of the astronomical forcing allows for synchronisation
over a wider range of parameters, compared to periodic forcing. Hence, glacial
cycles may conceivably have remained paced by the astronomical forcing
throughout the Pleistocene.
  However, all the models examined here also show a range of parameters for
which the structural stability of the ice age dynamics is weak. This means that
small variations in parameters or random fluctuations may cause significant
shifts in the succession of ice ages if the system were effectively in that
parameter range. Whether or not the system has strong structural stability
depends on the amplitude of the effects associated with the astronomical
forcing, which significantly differ across the different models studied here.
The possibility of synchronisation on eccentricity is also discussed and it is
shown that a high Rayleigh number on eccentricity, as recently found in
observations, is no guarantee of reliable synchronisation.
