http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.1641v1.pdf The glacial cycles are attributed to the climatic response of the orbital changes in the irradiance to the Earth (Milankovitch, 1930; Hays et al. , 1976). These changes in the forcing are to small to explain the observed climate variations as simple linear responses. Non-linear amplifications are necessary to account for the glacial cycles. Here an empirical model of the non-linear response is presented. From the model it is possible to assess the role of stochastic noise in comparison to the deterministic orbital forcing of the ice ages. The model is based on the bifurcation structure derived from the climate history. It indicates the dynamical origin of the Mid-Pleistocene transition (MPT) from the ’41 kyr world’ to the ’100 kyr world’. The dominant forcing in the latter is still the 41 kyr obliquity cycle, but the bifurcation structure of the climate system is changed.