Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

Embedding techniques provide a powerful advance in the development of experiment chaos. However there seems no universal method to find the best set of parameters to use. In this paper, we analyze the drawback of an algorithm of automatic embedding dimension and time delay presented in Reference^[1](Massayuki Otani and Antonia Jones, Oct. 2000), and propose a new approach for computing the embedding dimension and delay time based on the multiple autocorrelation and Γ-test. This approach is provided with a sound theoretic basis, and its computing complexity is relatively lower and not strongly depended on the data length. The experimental results indicate that a near optimum embeddingd imension and delay time can be estimated by using this approach, and the accuracy of invariants in phases space reconstruction is efficiently improved.