  The dynamics of glacial cycles is studied in terms of the dynamical systems
theory. We explore the dependence of the climate state on the phase of
astronomical forcing by examining five conceptual models of glacial cycles
proposed in the literature. The models can be expressed as quasiperiodically
forced dynamical systems. It is shown that four of them exhibit a strange
nonchaotic attractor (SNA), which is an intermediate regime between
quasiperiodicity and chaos. Then, the dependence of the climate state on the
phase of astronomical forcing is not given by smooth relations, but constitutes
a geometrically strange set. Our result suggests that the dynamics of SNA is a
candidate for the dynamics of glacial cycles, in addition to the well-known
dynamics of quasiperiodicity and chaos.
