University Of Tasmania
Browse
149465_Effects of periodic forcing on a paleoclimate delay model.pdf (8.8 MB)
Download file

Effects of periodic forcing on a paleoclimate delay model

Download (8.8 MB)
journal contribution
posted on 2023-05-21, 06:45 authored by Courtney QuinnCourtney Quinn, Sieber, J, von der Heydt, AS
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 due not 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, Krauskopf, and Osinga [SIAM J. Appl. Dyn. Syst., 3 (2004), pp. 161--190] into the equation-free framework by Kevrekidis and Samaey [Rev. Phys. Chem., 60 (2009), pp. 321--344].

History

Publication title

SIAM Journal on Applied Dynamical Systems

Volume

18

Pagination

1060-1077

ISSN

1536-0040

Department/School

School of Natural Sciences

Publisher

Society for Industrial and Applied Mathematics

Place of publication

United States

Rights statement

Copyright © 2019 Society for Industrial and Applied Mathematics

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences