# American Institute of Mathematical Sciences

2004, 1(1): 161-184. doi: 10.3934/mbe.2004.1.161

## Statistical properties of dynamical chaos

 1 Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, Saratov, Russian Federation, Russian Federation, Russian Federation, Russian Federation

Received  January 2004 Revised  March 2004 Published  March 2004

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. Mathematical Biosciences & Engineering, 2004, 1 (1) : 161-184. doi: 10.3934/mbe.2004.1.161
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