A method of detrended fluctuation analysis (DFA) is considered, which enables studying long-range correlations in non-stationary processes. Its modification is proposed that includes estimation of an additional quantity, namely, a scaling exponent characterizing the effects of non-stationarity in the experimental data. Using the dynamics of blood flow velocity in cerebral vessels as an example, the possibilities of a quantitative description of changes in the signal structure using the proposed modification of DFA are shown.

Improvement of the method of fluctuation analysis is performed, which includes taking into account the statistics of local standard deviations of the signal profile from piecewise linear approximation of the trend. It is shown that the proposed approach makes it possible to reduce the sensitivity of the method to single artifacts and increase the stability of the algorithm for computing the scaling exponent, which contributes to the wider use of the modified fluctuation analysis for solving problems of diagnosing complex processes in the dynamics of systems with time-varying characteristics.

We propose a method of estimating spectral properties of a system from short signals and processes with varying characteristics, which is based on the wavelet-transform modulus-maxima method. It is shown that this approach allows significant reduction of the computing error as compared with the classical spectral analysis.

The problem of increasing the accuracy of calculating the characteristics of complex dynamics in threshold systems is solved using the example of Lyapunov’s exponents. Despite the existence of theoretical and numerical studies that earlier have allowed one to substantiate the possibility of recovery of dynamic systems from the signals at the output of threshold systems, the problem of diagnostics of dynamics in the case of a small amount of data in the presence of noise requires a separate study. It has been shown how preliminary data processing that provides the transition to uniform sampling can significantly reduce the computation errors.