Statistical Description of Stochastic Dynamics.

Abstract

The main result of our research is the establishment of a general relationship for fluctuation of the spectral density of the chaotic motion which is similar to the Einstein fluctuation formula in statistical mechanics. A Gibbs-type partition of the chaotic motion is introduced. The distribution function of the spectral density defined on such partition is Gaussian. The variance of this distribution is the Fourier transform of the correlation function. This is demonstrated by direct numerical computations for the simple models of chaos. These results are the consequence of translational invariance and should be valid for the general case of chaotic motion described by differential equations.

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Document Details

Document Type
Technical Report
Publication Date
May 15, 1988
Accession Number
ADA192924

Entities

People

  • Alexander B. Rechester

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Availability
  • Computations
  • Delta Functions
  • Differential Equations
  • Distribution Functions
  • Dynamics
  • Equations
  • Invariance
  • Mechanics
  • New York
  • Physics
  • Power Spectra
  • Scientific Research
  • Spectra
  • Statistical Mechanics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.