Similarities of inter-point distance distributions on original and reconstructed attractors

State space reconstruction using time-delay coordinate systems is the most effective and significant technique for analyzing complex time series generated by nonlinear dynamical systems. In this study, we investigated the relationships between reconstruction parameters and the similarity of the structural properties of original and reconstructed attractors. In particular, we investigated the similarities between inter-point distance distributions on original and reconstructed attractors, while varying the reconstruction parameters for reconstructing a dynamical system using a time-delay coordinate system. The results show that the product of the reconstruction dimension and the time-delay should be constant to obtain high similarity.