Selection of parameters for phase space reconstruction of chaotic time series

Abstract

In order to model and predict the chaotic time series, one must choose appropriate delay time and embedding dimension for phase space reconstruction. Considering of the shortcomings of classical C-C method, a novel algorithm to select embedding window is investigated based on the improved C-C method in this paper. The mean correlation integral is defined in the novel algorithm. The dispersion between the mean correlation integral and statistical variable is used to eliminate the fluctuations apart from the local peaks. The embedding window is estimated firstly based on the pseudo-periodicity of the mean correlation integral. The delay time is estimated by the C-C method. The embedding dimension is obtained via the combined relation between the embedding window and delay time. The phase space reconstruction of two kinds of chaotic time series is carried out. The estimations of delay time and embedding dimension are in agree with those obtained using the saturated correlation dimension method. The results of simulations verify that the novel algorithm appears to be superior to other alternatives for determining the parameters of phase space reconstruction.