New method reveals hidden patterns in chaotic data with noisy signals.
The article presents a method to reconstruct chaotic time series with noise using high-order cumulants. It calculates the fractal dimension of chaotic sequences using a third-order cumulant, detects linear and nonlinear correlations to determine an embedding delay window, and calculates the embedding dimension and delay time to reconstruct the phase space. The method shows good robustness in calculating the embedding dimension of noisy chaotic sequences and produces well-extended strange attractors in the reconstructed phase space, reflecting the properties of multivariate chaotic sequences.
