2017/05/17 by Hans Engler, Hans G. Kaper, Tasso J. Kaper +1 · 26 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · #Ecosystem dynamics and resilience #Geology #Geology and Paleoclimatology Research #Geomorphology #Glacial period #Gravitational singularity #Ice sheet #Invariant (physics) #Marine and environmental studies #Mathematical analysis #Mathematical physics #Mathematics #Paleontology #Physics #Pleistocene #math.DS
paper · pdf · doi:10.1016/j.physd.2017.08.006
published in Physica D Nonlinear Phenomena 359, 1-20 (Elsevier BV) · 34 pages, 21 figures
arxiv created 2017/05/17 · openalex created_date 2017/05/26 · openalex publication_date 2017/08/24 · arxiv updated 2017/10/11 · openalex updated_date 2026/08/05
This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are well- separated, and they are center manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. This work was submitted March 30, 2017.