Abstract :
The analysis of complex signals from space and laboratory plasmas increasingly requires methods that go beyond conventional spectral and statistical techniques. This lecture presents a selection of modern approaches to time-series analysis inspired by concepts from nonlinear dynamics and chaos theory. The discussion begins with basic statistical characterization—probability distributions, moments, correlations, and power spectra—and progressively introduces methods capable of revealing nonlinear and dynamical properties hidden in apparently irregular signals.
As a first step, attention is given to correlation dimension and related entropy measures, which provide information about the effective dimensionality of the underlying dynamics, which quantify the complexity and temporal organization of fluctuations. Recurrence plots and recurrence quantification analysis are introduced as more sophisticated tools for visualizing and characterizing recurrent structures emerging in the phase space built by Takens procedure from experimental data. Finally, the lecture discusses permutation entropy of ordinal patterns, emphasizing the sensitivity of the computational procedure to noise and possible high-dimensionality of deterministic nature of the signals.
The methods are illustrated with examples from space and laboratory plasma measurements, including solar-wind and magnetospheric observations, planetary radio emissions, and laboratory plasma fluctuations. The emphasis is placed not only on the mathematical principles of the methods, but also on practical aspects of their application : data length and sampling, noise and parameter selection, statistical significance, surrogate testing, and the limitations of interpreting nonlinear measures from finite experimental datasets. The overall aim is to demonstrate how nonlinear-dynamics concepts can provide complementary information about the structure, complexity, and dynamical regime of plasma signals that may remain hidden in conventional signal-processing analyses.
Author :
Prof. Vladimir Ryabov, Complex & Intelligent systems department, University of Hakodate, Japan
Invited by Philippe Zarka in the context of Plas@Par
