This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the e ffect of noise on
dynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaotic
attractors and discuss methods of diagnosing the type of an attractor. We
consider regularities of the relaxation to an invariant probability measure for
diff erent types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunov
exponents, instantaneous phase di ffusion and the intensity of external noise.
Numeric results are compared with experimental data.
Citation: Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov. Statistical properties of dynamical chaos[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 161-184. doi: 10.3934/mbe.2004.1.161
Abstract
This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the e ffect of noise on
dynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaotic
attractors and discuss methods of diagnosing the type of an attractor. We
consider regularities of the relaxation to an invariant probability measure for
diff erent types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunov
exponents, instantaneous phase di ffusion and the intensity of external noise.
Numeric results are compared with experimental data.
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