Structural Stochastic Stability of a Simple Auto-Oscillatory Climatic Feedback System

Based on a previously developed more detailed model, governing possible feedbacks between sea ice extent ( eta ), deep ocean temperature ( theta ), and atmospheric carbon dioxide, a simple, deterministic, dynamical system for eta and theta which yields a stable limit cycle as a solution was constructed. To make the system more realistic, random (white noise) forcing was added and the new response was explored as a function of the amplitude of this stochastic forcing. Included in the analysis are examples of sample time series, sample phase trajectories, variance spectra, and residence density in the phase space. The results show that physically reasonable values of the stochastic amplitude do not completely obscure the basic limit cycle but do convert an intransitive, deterministic system to an almost intransitive one that tends to reside longer in two distinct regions of the phase space, with relatively fast transitions between them. The solutions also show how stochastic forcing of one component of the climatic feedback system (i.e., eta ) can lead to a damped response in another unforced component ( theta ).