Reviews of topical problems

Statistical properties of dynamical chaos

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International Research Institute of Nonlinear Dynamics, Department of Physics, N.G. Chernyshevskii; Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russian Federation

Statistical descriptions of dynamical chaos and investigations of noise effects on chaotic oscillation regimes are reviewed. Nearly hyperbolic and nonhyperbolic chaotic attractors are studied. An illustration of the technique of diagnosing the attractor type in numerical simulations is given. Regularities in relaxation to the invariant probability distribution are analyzed for various types of attractors. Spectral-correlative properties of chaotic oscillations are investigated. Decay laws for the autocorrelation functions and the shapes of the power spectra are found, along with their relationship to the Lyapunov exponents, diffusion of the instantaneous phase, and the intensity of external noise. The mechanism of the onset of chaos and its relationship to the characteristics of the spiral attractors are demonstrated for inhomogeneous media that can be modeled by the Ginzburg-Landau equation. Numerical data are compared with experimental results.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 02.50.−r, 05.45.−a, 47.52.+j (all)
DOI: 10.1070/PU2005v048n02ABEH002070
Citation: Anishchenko V S, Vadivasova T E, Okrokvertskhov G A, Strelkova G I "Statistical properties of dynamical chaos" Phys. Usp. 48 151–166 (2005)
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Оригинал: Анищенко В С, Вадивасова Т Е, Окрокверцхов Г А, Стрелкова Г И «Статистические свойства динамического хаоса» УФН 175 163–179 (2005); DOI: 10.3367/UFNr.0175.200502c.0163

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