期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 292, 期 -, 页码 70-83出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2014.11.003
关键词
Mixed-mode oscillations; MMO; Fast/slow; Folded node; Glacial cycle; Paleoclimate
资金
- Mathematics and Climate Research Network on NSF [DMS-0940363, DMS-1239013]
- MCRN on NSF [DMS-0940363]
- University of Arizona from HHMI [52006942]
- Australian Research Counsel [FT120100309]
- Australian Research Council [FT120100309] Funding Source: Australian Research Council
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0940363] Funding Source: National Science Foundation
Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where is an element of = 0. In this parameter regime, the model has a stable periodic orbit of type 1(s) for some s > 0. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern. (C) 2014 Elsevier B.V. All rights reserved.
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