Flicker-Noise Spectroscopy for Analyzing Chaotic Time Series of Dynamic Variables: Problem of Signal-to-Noise Relation

Abstract

The underlying principles of flicker-noise spectroscopy (FNS), which is a new method for obtaining information contained in chaotic time signals, are presented. The method's essence is the imparting of an information value to sequences of distinguishable irregularities (spikes, jumps, discontinuities of derivatives of various orders) in dynamic variables that characterize systems under test. The information distinguishability of the types of irregularities introduced here follows from the fact that the “passport data” that characterize the aggregate properties of the irregularities are distinguishably extracted when analyzing power spectra and difference momenta (“structural functions”) of different orders. Shown are potentialities of the FNS method associated with the introduction of quantitative criteria for the nonstationarity of time series produced by real systems. Revealing such criteria is of interest in connection with the all-pervading character of the nonstationarity phenomenon and with the search for “harbingers” of most dramatic changes in the state of evolving systems. The FNS method may be used for extracting phenomenological properties when analyzing time series that characterize evolution of complex systems. As an example, the dynamics of the electric potential fluctuation in an electromembrane system with a cation-exchange membrane in the region of the overlimiting current is considered. The introduced techniques of parametrization of a chaotic signal may effectively be used for the signal isolation against a “noisy” background even in the case where in fact one has to solve the problem of the isolation of two informatively-valuable signals if the information concerning parameters of the target signal is prespecified.