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Chaotic time series analysis. (English) Zbl 1191.37046
Summary: Chaotic dynamical systems are ubiquitous in nature and most of them does not have an explicit dynamical equation and can be only understood through the available time series. We here briefly review the basic concepts of time series and its analytic tools, such as dimension, Lyapunov exponent, Hilbert transform, and attractor reconstruction. Then we discuss its applications in a few fields such as the construction of differential equations, identification of synchronization and coupling direction, coherence resonance, and traffic data analysis in Internet.
MSC:
37M10Time series analysis (dynamical systems)
37D45Strange attractors, chaotic dynamics
37N99Applications of dynamical systems
68M11Internet topics