  This review presents the fundamentals of Flicker-Noise Spectroscopy (FNS), a
general phenomenological methodology in which the dynamics and structure of
complex systems, characterized by nonlinear interactions, dissipation, and
inertia, are analyzed by extracting information from various signals with
stochastically varying components generated by the systems. The basic idea of
FNS is to treat the correlation links present in sequences of different
irregularities, such as spikes, "jumps", and discontinuities in derivatives of
different orders, on all levels of the spatiotemporal hierarchy of the system
under study as main information carriers. The tools to extract and analyze the
information are power spectra and difference moments (structural functions) of
various orders. Presently, FNS can be applied to three types of problems: (1)
determination of parameters or patterns that characterize the dynamics or
structural features of complex systems; (2) finding precursors of abrupt
changes in the state of various complex systems based on a priori information
about the dynamics of the systems; and (3) determination of flow dynamics in
distributed systems based on the analysis of dynamic correlations in stochastic
signals that are simultaneously measured at different points in space. Examples
of FNS applications to such problems as parameterization of the images produced
with atomic force microscopy (AFM), determination of precursors for electric
breakdowns and major earthquakes, and analysis of electric potential
fluctuations in electromembrane systems, as well as to some other problems in
electrochemistry and medicine are discussed.

Data Analysis, Statistics and Probability;Chemical Physics