Construction of dynamical models for processes with a high dimension of the embedding space

A method is proposed for the construction of empirical dynamical models for processes with a high-dimension of the embedding space. It is shown that t he higher dynamical degrees of freedom of a process observed can be taken i nto consideration by generalizing third-order differential equations in the class of equations with delayed argument. A method is proposed for the dec omposition of the state vector of the observed process and for the effectiv e estimation of the dimension of the embedding space. An example of the con struction of the empirical model is presented for a quasi-stationary segmen t of an actual electroencephalogram (EEG) of a human.