External Forcing Extraction of Continuous Systems Based on Slow Feature Analysis

The influence of gradual external forcing changes on non-stationary system is significant, and the manner by which external forcing features are reconstructed from non-stationary system has become the key to study the dynamic characteristics of the system. In this study, a continuous system (the modified Lorenz system) is used as the reference model, based on the slow feature analysis (SFA). We discuss the ability of SFA in extracting different forcing signals in the model under conditions of periodic forcing, weakened periodic forcing, exponential decay forcing, and periodic forcing with exponential decay. Results show that the SFA method can extract external forcing information acting on the continuous system and its extraction effect is correlated to the intensity of the external forcing, noise, and embedding dimension m: The weaker the external forcing or the stronger the noise interference, the worse the extraction effect. Hence, the false high-frequency fluctuation appears in the extracted signal. The increase in embedding dimension m can improve the extraction effect of the external forcing signal to a certain extent. The results also shows that the external forcing acting on a single variable embeds its driving information in the system and SFA can extract the external forcing signal from other variables.