Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial–interglacial cycles

Abstract

Glacial–interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is ∼40 kyr before the so-called middle Pleistocene transition between ∼1.2 and ∼0.7 Myr ago, and it is ∼100 kyr after the transition. In this paper, the dynamics of glacial–interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle–node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.