Determination of phase-space reconstruction parameters of chaotic time series

A new method called C–C–1 method is suggested, which can improve some drawbacks of the original C–C method. Based on the theory of period N , a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N, r, t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a quantity ∆S2(t) is needed to ascertain the optimal delay time. The parameter of the C–C method – embedding dimensionm – is adjusted rationally. In the new method, the estimates of the optimal delay time and the optimal delay time window are more appropriate. The robustness of the C– C–1 method reaches 40%, whereas that of the C–C method is 30%.