Statistical properties of dynamical chaos
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.
|