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A minimal conceptual model for glacial-interglacial cycles.

Jade Ajagun-Brauns1, Peter Ditlevsen1

  • 1Niels Bohr Institute, University of Copenhagen , Copenhagen, Denmark.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 18, 2026
PubMed
Summary

Pleistocene glacial cycles exhibit complex dynamics, not a simple linear response to astronomical forcing. A new model explains the Mid-Pleistocene Transition and sawtooth glacial cycles through internal climate system changes.

Keywords:
dynamical systemsice agespaleoclimate

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Area of Science:

  • Earth and Climate Sciences
  • Complex Systems Dynamics
  • Paleoclimatology

Background:

  • Pleistocene glacial cycles are driven by astronomical variations in solar radiation (insolation).
  • The climate system's response to these variations is nonlinear, involving intricate internal dynamics.
  • The Mid-Pleistocene Transition (MPT) marks a shift from ~41,000-year cycles to ~100,000-year cycles.

Purpose of the Study:

  • To test the hypothesis that a structural change in a conceptual glacial cycle model explains the MPT.
  • To investigate if a slow control parameter governs the transition and post-MPT glacial cycle characteristics.
  • To provide numerical solutions for MacAyeal's nonlinear differential equation model of glacial cycles.

Main Methods:

  • Numerical computation of solutions for MacAyeal's nonlinear differential equation model.
  • Analysis of model behavior under variation of a slow control parameter, 'α'.
  • Testing the model's ability to reproduce time-asymmetric (sawtooth) glacial cycles post-MPT.

Main Results:

  • The study presents the first numerical solutions for MacAyeal's conceptual glacial cycle model.
  • A slow control parameter ('α') is shown to govern a structural change, explaining the MPT.
  • The model successfully reproduces time-asymmetric, sawtooth-shaped glacial cycles observed after the MPT.

Conclusions:

  • A structural change, driven by a slow control parameter, provides a viable explanation for the Mid-Pleistocene Transition.
  • The nonlinear dynamics of the climate system, as modeled, are crucial for understanding glacial cycle evolution.
  • This work validates and extends MacAyeal's conceptual model, offering insights into paleoclimate dynamics.