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 the 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 the astronomical forcing is not given by smooth relations, but constitutes a geometrically strange set. Our result suggests that SNA is a candidate for representing the dynamics of glacial cycles, in addition to well-known quasiperiodicity and chaos.