TY - CHAP

T1 - Modeling the Dynamics of Glacial Cycles

AU - Engler, Hans

AU - Kaper, Hans G.

AU - Kaper, Tasso J.

AU - Vo, Theodore

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-22044-0_1

DO - 10.1007/978-3-030-22044-0_1

M3 - Chapter (Book)

SN - 9783030220433

VL - 5

T3 - Mathematics of Planet Earth

SP - 3

EP - 33

BT - Mathematics of Planet Earth

A2 - Kaper, Hans

A2 - Roberts, Fred

PB - Springer

CY - Cham Switzerland

ER -