Paleoclimate time series extracted from deep-sea sediment and ice cores exhibit frequent episodes of abrupt climate change believed to be the result of nonlinear response of the climate system to internal or external forcing, yet, neither the physical mechanisms nor the nature of the nonlinearities involved are well understood. At the orbital (10-100kyr) and millennial scales, abrupt climate change appears as sudden, rapid global warming events, each followed by periods of slow cooling. The sequence often forms a distinctive saw-tooth shaped time series, epitomized by the deep-sea records of the last million years and the Dansgaard-Oeschger (D/O) oscillations of the last glacial.

Here I introduce a simplified mathematical model consisting of a novel arrangement of coupled nonlinear differential equations that appears to capture some important physics of climate change, closely reproducing the saw-tooth shape of the deep-sea sediment and ice core time series, the relatively abrupt mid-Pleistocene climate switch, and the intriguing D/O oscillations. The nonlinearity in the model consists of competing positive and negative delayed feedbacks and nonlinear coupling between temperature and ice extent. These simple mechanisms are apparently enough to simulate important features in the time series, including rapid global warming. The close fit with the available data suggests that the D/O oscillations are entrained by the third harmonic of the precession forcing, and by the precession itself, but the response is intermittent, occurring at separate intervals within the noise. From the point of view of nonlinear dynamics of complex systems it appears as if the Greenland's ice core record of the last ~100kyr reflects a climate system operating at the edge between order and chaos; that is, between a recognizable (albeit nonlinear) response to astronomical forcing and self-generated random noise. Within the orderly intervals the model closely replicates the D/O and generates a persistent ~1.5kyr spectral sideband, apparently produced by frequency modulation of the natural oscillation of Greenland’s ice cap and its associate climate.