  The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr
glacial-interglacial cycles that occurred roughly 1 Myr ago, is often
considered as a change in internal climate dynamics. Here we revisit the model
of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988).
We show that it is quantitatively similar to a scalar equation for the ice
dynamics only when combining the remaining components into a single delayed
feedback term. The delay is the sum of the internal times scales of ocean
transport and ice sheet dynamics, which is on the order of 10 kyr. We find
that, in the absence of astronomical forcing, the delayed feedback leads to
bistable behaviour, where stable large-amplitude oscillations of ice volume and
an equilibrium coexist over a large range of values for the delay. We then
apply astronomical forcing. We perform a systematic study to show how the
system response depends on the forcing amplitude. We find that over a wide
range of forcing amplitudes the forcing leads to a switch from small-scale
oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr
without any change of other parameters. The transition in the forced model
consistently occurs near the time of the Mid-Pleistocene Transition as observed
in data records. This provides evidence that the MPT could have been primarily
a forcing-induced switch between attractors of the internal dynamics. Small
additional random disturbances make the forcing-induced transition near 800 kyr
BP even more robust. We also find that the forced system forgets its initial
history during the small-scale oscillations, in particular, nearby initial
conditions converge prior to transitioning. In contrast to this, in the regime
of large-amplitude oscillations, the oscillation phase is very sensitive to
random perturbations, which has a strong effect on the timing of the
deglaciation events.

Atmospheric and Oceanic Physics;Dynamical Systems;Chaotic Dynamics