Modeling the Dynamics of Glacial Cycles

Hans Engler, Hans G. Kaper, Tasso J. Kaper, Theodore Vo

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-review


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.
Original languageEnglish
Title of host publicationMathematics of Planet Earth
Subtitle of host publicationProtecting Our Planet, Learning from the Past, Safeguarding for the Future
EditorsHans Kaper, Fred Roberts
Place of PublicationCham Switzerland
Number of pages31
ISBN (Electronic)9783030220440
ISBN (Print)9783030220433
Publication statusPublished - 2019

Publication series

NameMathematics of Planet Earth
ISSN (Print)2524-4264
ISSN (Electronic)2524-4272

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