Application of high-order cumulant in the phase-space reconstruction of multivariate chaotic series

Aimed at multivariate chaotic time series with random noise, this paper builds a noisy multivariate phase space reconstruction method making use of the noise robustness of high-order cumulants. First, the local intrinsic dimension (LID) is selected as the fractal dimension of chaotic sequences, which has a fairly good robustness to noise. A third-order cumulant is introduced into the fractal dimension calculation. Second, both the linear correlations and the nonlinear correlations of each component are detected to initialize an embedding delay window. Finally, the embedding dimension and delay time are calculated to reconstruct the phase space of multivariate. The simulation results of x and y sequences produced by Lorenz equation show that the method proposed in the paper has a good robustness in the calculation of the noisy chaotic sequence´s embedding dimension, and the reconstructed strange attractors get good extension in the reconstructed phase space, which better reflects the phase space properties of the multivariate chaotic sequence.