  This article is concerned with the internal dynamics of a conceptual model
proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to
explain central features of the glacial cycles observed in the climate record
of the Pleistocene Epoch. It is shown that, in most parameter regimes, the
long-term system dynamics occur on certain intrinsic two-dimensional invariant
manifolds in the three-dimensional state space. These invariant manifolds are
slow manifolds when the characteristic time scales for the total global ice
mass and the volume of North Atlantic Deep Water are well- separated, and they
are center manifolds when the characteristic time scales for the total global
ice mass and the volume of North Atlantic Deep Water are comparable. In both
cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens
singularities, and the bifurcation curves associated to these singularities
organize the parameter regions in which the model exhibits glacial cycles.
  This work was submitted March 30, 2017.
