A dynamical systems approach to the Pleistocene climate - Part I of II

In 1990, K. Maasch and B. Saltzman introduced a three-dimensional dynamical system to explain the glacial cycles of the Pleistocene Epoch. The model incorporates interactions between the Earth's oceans, atmosphere, and cryosphere. They showed numerically that a particular slow drift of some of the system parameters, together with orbital forcing, can result in system behavior that exhibits the mid-Pleistocene transition to large-amplitude limit cycles, plausible temporal wave forms for ice and CO2, and correct phase relations between the system variables. In this presentation, we briefly review the Maasch-Saltzman model and show that a reduced two-dimensional version of the model already exhibits the most salient dynamical features of the full model. In particular, we show that there exist large-amplitude limit cycles in a large portion of the parameter space.