Effects of periodic forcing on a Paleoclimate delay model

TL;DR

This paper investigates how periodic forcing influences a delay differential equation model of the Mid-Pleistocene Transition, revealing that forcing can induce a regime shift through basin boundary shifts rather than bifurcations.

Contribution

It introduces a novel analysis of forcing effects on a Paleoclimate delay model, demonstrating basin shifts as the mechanism for regime transitions.

Findings

Forcing causes sudden regime shifts in the model.

Transition is due to basin boundary shifts, not bifurcations.

A new computational method for basin boundary analysis in DDEs is proposed.

Abstract

We present a study of a delay differential equation (DDE) model for the Mid-Pleistocene Transition (MPT). We investigate the behavior of the model when subjected to periodic forcing. The unforced model has a bistable region consisting of a stable equilibrium along with a large amplitude stable periodic orbit. We study how forcing affects solutions in this region. Forcing based on astronomical data causes a sudden transition in time and under increase of the forcing amplitude, moving the model response from a non-MPT regime to an MPT regime. Similar transition behavior is found for periodic forcing. A bifurcation analysis shows that the transition is not due to a bifurcation but instead to a shifting basin of attraction. While determining the basin boundary we demonstrate how one can accurately compute the intersection of a stable manifold of a saddle with a slow manifold in a DDE by embedding the algorithm for planar maps proposed by England et al. (SIADS 2004(3)) into the equation-free framework by Kevrekidis et al. (Rev. Phys. Chem. 2009 (60)).