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

TL;DR

This paper models glacial-interglacial cycles using a phase oscillator influenced by insolation, revealing bifurcations and the emergence of strange nonchaotic attractors that explain the variability in cycle periodicity.

Contribution

It introduces a phase oscillator model that captures bifurcations and strange nonchaotic attractors in glacial cycles, linking mathematical dynamics to climate variability.

Findings

Mode-locking likely for 41 kyr cycles

Strange nonchaotic attractors appear through nonsmooth bifurcations

Sensitivity of 100 kyr cycles to parameter changes when attractors are present

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 $\sim $40 kyr before the so-called middle Pleistocene transition between $\sim$1.2 and $\sim$0.7 Myr ago, and it is $\sim $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.