# Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles

## TL;DR

This paper analyzes the internal dynamics of the Maasch-Saltzman model for glacial cycles, revealing how invariant manifolds and bifurcations organize the model's ability to produce glacial oscillations.

## Contribution

It provides a dynamical systems analysis of the Maasch-Saltzman model, identifying invariant manifolds and bifurcation structures that explain glacial cycle behavior.

## Key findings

- Long-term dynamics occur on invariant manifolds.
- Bogdanov-Takens bifurcations govern the reduced dynamics.
- Parameter regions for glacial cycles are organized by bifurcation curves.

## Abstract

This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are well- separated, and they are center manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. This work was submitted March 30, 2017.