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Keywords:

  • auto-oscillation;
  • temperature variation multifractal structure;
  • climate self-organization;
  • astronomical cycles

Abstract

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.