This chapter is concerned with the dynamics of glacial cycles observed in the geological record of the Pleistocene Epoch. It focuses on a conceptual model proposed by Maasch and Saltzman (J Geophys Res 95(D2):1955–1963, 1990), which is based on physical arguments and emphasizes the role of atmospheric CO2 in the generation and persistence of periodic orbits (limit cycles). The model consists of three ordinary differential equations with four parameters for the anomalies of the total global ice mass, the atmospheric CO2 concentration, and the volume of the North Atlantic Deep Water. In this chapter, it is shown that a simplified two-dimensional symmetric version displays many of the essential features of the full model, including equilibrium states, limit cycles, their basic bifurcations, and a Bogdanov–Takens point that serves as an organizing center for the local and global dynamics. Also, symmetry breaking splits the Bogdanov–Takens point into two, with different local dynamics in their neighborhoods.
|Title of host publication||Mathematics of Planet Earth|
|Subtitle of host publication||Protecting Our Planet, Learning from the Past, Safeguarding for the Future|
|Editors||Hans Kaper, Fred Roberts|
|Place of Publication||Cham Switzerland|
|Number of pages||31|
|Publication status||Published - 2019|
|Name||Mathematics of Planet Earth|