  It is well known that periodic forcing of a nonlinear system, even of a
two-dimensional autonomous system, can produce chaotic responses with sensitive
dependence on initial conditions if the forcing induces sufficient stretching
and folding of the phase space. Quasiperiodic forcing can similarly produce
chaotic responses, where the transition to chaos on changing a parameter can
bring the system into regions of strange non-chaotic behaviour. Although it is
generally acknowledged that the timings of Pleistocene ice ages are at least
partly due to Milankovitch forcing (which may be approximated as quasiperiodic,
with energy concentrated near a small number of frequencies), the precise
details of what can be inferred about the timings of glaciations and
deglaciations from the forcing is still unclear. In this paper, we perform a
quantitative comparison of the response of several low-order nonlinear
conceptual models for these ice ages to various types of quasiperiodic forcing.
By computing largest Lyapunov exponents and mean periods, we demonstrate that
many models can have a chaotic response to quasiperiodic forcing for a range of
forcing amplitudes, even though some of the simplest conceptual models do not.
These results suggest that pacing of ice ages to forcing may have only limited
determinism.
