Identification of chaotic systems using fractal dimension of the reconstructed attractor

The problem of identifying chaotic systems is considered. Dimensions of chaotic attractors are briefly discussed. An algorithm based on the attractor´s local intrinsic dimensionality (LID) is discussed and implemented using singular value decomposition and some thresholding techniques. The LID will produce an upper bound on the fractal dimension. The problem of data corrupted by noise is considered. Simulations are performed using standard chaotic signals, and a comparison is made between the LID approach and the Grassberger-Procaccia algorithm