Dynamics between order and chaos in conceptual models of glacial cycles

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.