  Glacial-interglacial cycles are large variations in continental ice mass and
greenhouse gases, which have dominated climate variability over the Quaternary.
The dominant periodicity of the cycles is $\sim $40 kyr before the so-called
middle Pleistocene transition between $\sim$1.2 and $\sim$0.7 Myr ago, and it
is $\sim $100 kyr after the transition. In this paper, the dynamics of
glacial-interglacial cycles are investigated using a phase oscillator model
forced by the time-varying incoming solar radiation (insolation). We analyze
the bifurcations of the system and show that strange nonchaotic attractors
appear through nonsmooth saddle-node bifurcations of tori. The bifurcation
analysis indicates that mode-locking is likely to occur for the 41 kyr glacial
cycles but not likely for the 100 kyr glacial cycles. The sequence of
mode-locked 41 kyr cycles is robust to small parameter changes. However, the
sequence of 100 kyr glacial cycles can be sensitive to parameter changes when
the system has a strange nonchaotic attractor.
