2018/08/07 by Courtney Quinn, Quinn, Courtney, Jan Sieber +3 · 1 citation
Mathematics · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #math.DS #nlin.CD #physics.ao-ph
paper · pdf · doi:10.48550/arxiv.1808.02310
18 pages, supplementary material available on https://doi.org/10.6084/m9.figshare.7048292.v1
arxiv created 2019/01/11 · arxiv updated 2019/01/14
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)).