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

2015/05/22 by T. Mitsui, Takahito Mitsui, Michel Crucifix +1 · 52 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Attractor #Climatology #Ecosystem dynamics and resilience #Geology #Geology and Paleoclimatology Research #Glacial period #Ice age #Interglacial #Marine and environmental studies #Mathematics #Paleontology #Physics #Pleistocene #nlin.CD #physics.ao-ph #physics.geo-ph

paper · pdf · doi:10.1016/j.physd.2015.05.007

published in Physica D Nonlinear Phenomena 306, 25-33 (Elsevier BV) · 25 pages, 9 figures

openalex publication_date 2015/05/22 · arxiv created 2015/06/15 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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

Citations

• A Pliocene‐Pleistocene stack of 57 globally distributed benthic δ18O records
• Long-Term Variations of Daily Insolation and Quaternary Climatic Changes
• Insolation values for the climate of the last 10 million years
• On the Structure and Origin of Major Glaciation Cycles 1. Linear Responses to Milankovitch Forcing
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• Fractalization of Torus Revisited as a Strange Nonchaotic Attractor
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• Synchronization of strange nonchaotic attractors