анализ временных рядов

Purpose. Purpose of this article is to review recent results (over the past three years) obtained at the Institute of Applied Physics (IAP RAS) relating of applications of the method for constructing optimal empirical models to climatic systems. Methods. This method, developed by the authors of the article, includes the construction of reduced models of the system under study in the form of random dynamical systems.

We propose a new method for analysis of electroencephalograms. It is based on construction of a parameterized stochastic model of the observed process (evolution operator). A certain functional form of the evolution operator is proposed. This form describes deterministic properties of the investigated process, as well as stochastic ones. The parameters of the evolution operator are reconstructed from the experimental data by using the Bayesian approach. New («fast») dynamical variables, which allow for the peculiar features of electroencephalogram, are found.

The methods are proposed for the reconstruction of time-delay systems modeled by neutral delay-differential equations from their time series. The methods are successfully applied to the recovery of generalized Mackey–Glass equation and equations modeling ship rolling and human movement from simulated data.

The method is proposed for delay time estimation in time-delay systems from their time series. The method is based on the nearest neighbor method. It can be applied to a wide class of time-delay systems and it is still efficient under very high levels of dynamical and measurement noise.

Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

The methods for the reconstruction of model delay-differential equations for ensembles of coupled time-delay systems from their time series are proposed. The methods efficiency is illustrated using chaotic and periodic time series from chains of diffusively coupled model and experimental time-delay systems for the cases of unidirectional andmutual coupling.

Purpose. To suggest a new approach to reconstruction of couping architecture and individual parameters of first-order time-delayed oscillators from experimental series of their oscillations. Method. The method is based on minimization of target function, which characterizes a distance between points of nonlinear function of a current oscillator, which is to be reconstructed. Then estimated coupling coefficients are split into significant and insignificant. Minimization of target function is processed with least squares routine.

Time-delayed systems, including coupled ones, became popular models of different physical and biological objects. Often One or few variables of such models cannot be directly measured, these variables are called hidden variables. However, reconstruction of models from experimental signals in presence of hidden variables can be very suitable for model verification and indirect measurement.