Attractor dimension of nonstationary dynamical systems from small data sets

Abstract

Several sources of error in the calculation of attractor dimension from time series by the Grassberger and Procaccia or similar algorithms can be avoided or minimized by appropriate choice of algorithm and of criteria for selection of parameter values. Some problems and means of avoiding them are demonstrated, and statistical results are presented for dimension calculated from many independent sets of each of a wide range of data set size, to show that sets of a few hundred vectors or even less are useful for dimension calculation. This method with small data sets is shown to be effective in following changes in attractor dimension of a nonstationary dynamical system.