Studies in Chaos Using Stochastic Methods

Abstract

Methods of chaos have been used to classify many heretofore inexplicable nonlinear dynamical systems in fields as diverse as ecology to engineering and economics to meteorology. This thesis presents the mathematical background needed to understand chaos as well as the engineering techniques used to study the nature of dynamical systems. Several dynamical systems are studied using two probabilistic measures of chaos, fractal correlation dimension and the multivariate scaling analysis. A new technique for developing a multivariate scaling analysis using a time embedding procedure is presented. The dynamical systems studied include the Lorenz equations, Duffing's equation and helicopter flight vibrations.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1991
Accession Number
ADA246919

Entities

People

  • Edward A. Healy Jr

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computer Simulations
  • Computers
  • Differential Equations
  • Frequency
  • Frequency Domain
  • Nonlinear Dynamics
  • Nonlinear Systems
  • Normal Distribution
  • Numerical Integration
  • Probability Density Functions
  • Random Variables
  • Stochastic Processes
  • Theorems
  • Two Dimensional
  • United States Military Academy

Fields of Study

  • Physics

Readers

  • Control Systems Engineering.
  • Theoretical Analysis.