A simplified version of a previously described dynamical model governing global ice mass, atmospheric carbon dioxide, and mean ocean temperature (that may also be a proxy for some other CO2-controlling oceanic variable, eg nutrient supply) is shown to possess solutions, in a realistic parameter range, that can replicate the main features of the climatic variations implied by the full, 2Ma, Quaternary oxygen isotope record. The model contains only 3 free parameters in this simplified form. No external earth-orbital forcing is prescribed; ie the model represents only internal dynamics. The present results, therefore, constitute a first-order account for the existence of the 'ice age' fluctuations over the last 2Ma, including the concomitant variations of atmospheric CO2. The variations of mean ocean temperature (or a related CO2-controlling proxy variable) are also deduced and represent a side prediction of the model.
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Saltzman et al. (1987) studied this question.