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. 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 are interested in how forcing affects solutions in this region. The results here are compared to what is found when the model is forced with the quasiperiodic insolation. The quasiperiodic forcing displays a threshold behavior when the forcing amplitude is increased - moving the model from a non-transitioning regime to a transitioning regime. Similar threshold behavior is found when the periodic forcing amplitude is increased. A bifurcation analysis shows that the threshold is not due to a bifurcation but instead to a shifting basin of attraction.