  In this paper we perform a careful analysis of the forced PP04 model for
climate change, in particular the behaviour of the ice-ages. This system models
the transition from a glacial to an inter-glacial state through a sudden
release of oceanic Carbon Dioxide into the atmosphere. This process can be cast
in terms of a Filippov dynamical system, with a discontinuous change in its
dynamics related to the Carbon Dioxide release. By using techniques from the
theory of non-smooth dynamical systems, we give an analysis of this model in
the cases of both no insolation forcing and also periodic insolation forcing.
This reveals a rich, and novel, dynamical structure to the solutions of the
PP04 model. In particular we see synchronised periodic solutions with subtle
regions of existence which depend on the amplitude and frequency of the
forcing. The orbits can be created/destroyed in both smooth and discontinuity
induced bifurcations. We study both the orbits and the transitions between them
and make comparisons with actual climate dynamics.
