Discriminant procedure for dynamical equation reconstruction from noisy experimental data and for revealing nonstationarity in chaotic systems

Discriminant procedure developed in 30-thies and dealing with two time-window statistical analysis of time series is generalized for studying nonstationary chaotic processes. For these purposes discriminant function is to be chosen in the form of model dynamical equation with indefinite coefficients, which are to be determined from Fisher's minimax criterion. Thereby the dynamical equation for a system under consideration can be recovered. The optimal length of a sample is shown to be comparable with the interval of predictability. It is shown also, that low dimensional dynamical models for the studied process are able to reveal nonstationarity even from chaotic time series of high dimension. The suggested method can be applied to analysis of hidden communication systems with chaotic carrier, heart rhythms nonstationarity and other physical and biophysical systems.