Effects of Periodic Forcing on a Paleoclimate Delay Model

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].