Characterizing chaotic attractors using fourth-order off-diagonal cumulant slices

Local intrinsic dimension (LID) is a new approach to characterize chaotic signals. This method demonstrates more robustness to noise than the traditional fractal dimension (FD) estimation algorithms such as the Grassberger and Procaccia algorithm (GPA). In order to form the attractor in the phase space, the one-dimensional time-series of a signal needs to be embedded in a higher dimension. A significant limitation of the LID methods and the traditional FD methods is their sensitivity to the size of the higher embedding dimension (r) in the presence of noise. A new estimation method of the LID using higher-order statistics is proposed for chaotic signals corrupted by additive noise. In this work, estimation of the LID is based on the fourth-order, off-diagonal cumulant matrix and is shown to be less sensitive to noise and the size of the embedding dimension