Journal of Applied Mathematics and Decision Sciences
Volume 5 (2001), Issue 4, Pages 201-214

Long-term global climate dynamics: A Hopf bifurcation causing recurrent ice ages

Andrei Korobeinikov and Alex Mcnabb

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

Copyright © 2001 Andrei Korobeinikov and Alex Mcnabb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Rapid and dramatic changes in climate and glacial conditions have taken place during the last 2.5 million years of the earth's history. Huge ice sheets expanded and contracted periodically, at times covering large areas of North America and Europe. Global sea levels dropped and rose 100 m to 150 m in response to the growth and melting of glaciers, causing continental coast lines to move far into present sea areas and then retreated again. We will use a simple conceptual model to demonstrate that these climate and glacier fluctuations can be a consequence of a supercritical Hopf bifurcation in models of the “ocean-land-atmosphere” system.