  The Late Pleistocene Antarctic temperature variation curve is decomposed into
two components: cyclic and high frequency, stochastic. For each of these
components, a mathematical model is developed which shows that the cyclic and
stochastic temperature variations are distinct, but interconnected, processes
with their own self-organization. To model the cyclic component, a system of
ordinary differential equations is written which represent an auto-oscillating,
self-organized process with constant period. It is also shown that these
equations can be used to model more realistic variations in temperature with
changing cycle length. For the stochastic component, the multifractal spectrum
is calculated and compared to the multifractal spectrum of a critical
sine-circle map. A physical interpretation of relevant mathematical models and
discussion of future climate development within the context of this work is
given.
