A Study on Methods for Determining Phase Space Reconstruction Parameters

Abstract

Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chen's attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex autocorrelation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex autocorrelation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified by combing the application of the correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.