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