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Effects of periodic forcing on a paleoclimate delay model

Citation

Quinn, C and Sieber, J and von der Heydt, AS, Effects of periodic forcing on a paleoclimate delay model, SIAM Journal on Applied Dynamical Systems, 18, (2) pp. 1060-1077. ISSN 1536-0040 (2018) [Refereed Article]


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Copyright 2019 Society for Industrial and Applied Mathematics

DOI: doi:10.1137/18M1203079

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 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].

Item Details

Item Type:Refereed Article
Keywords:delay, paleoclimate, bifurcation, Mid-Pleistocene Transition, equation-free methods, dimension reduction
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Dynamical systems in applications
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Quinn, C (Dr Courtney Quinn)
ID Code:149465
Year Published:2018
Web of Science® Times Cited:3
Deposited By:Mathematics
Deposited On:2022-03-31
Last Modified:2022-05-26
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