Selection of Delay Time Window and Delay Time in Phase Space Reconstruction

A new method called C-C-3 method is suggested, which can amend at least 4 drawbacks of the C-C method (which is a popular method of the phase space reconstruction). The correlation integral algorithm of the time series is improved; and based on the theory of the chaotic system period N, the first local minimum of S3_cor(t) which can show the period N of the chaotic time series is looked for, and by which the optimal delay time window can be determined. Only the first local minimum of the average S3(t) is wanted to estimate the optimal delay time. The results by the new method are more stable and more appropriate. Furthermore, The robustness of the C-C-3 method reaches 70%, whereas that of the C-C method is 30%. Keywords: Delay Time Window; Delay Time; Correlation Integral; Phase Space Reconstruction