Application of Time-Delay Reconstruction Method for Examination of Spatial Inhomogeneity of Dynamical Systems

Three spatially extended one-dimensional dynamical systems are examined by numerical simulations and the time-delay technique is applied to find their dynamics at different positions in space. On the basis of this technique the correlation dimension is calculated from time series obtained at different positions. It is found that the value of the correlation dimension may vary from one position to another, reflecting the spatial inhomogeneity of the system